texonom/texonom-md · Datasets at Hugging Face

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Jacobian Matrix	Matrix Usages	Jun 2, 2023	Alan Jo	Alan Jo	Jun 2, 2023		행렬의 원소들은 모두 1차 미분 계수로 구성 즉 미소 변화에 관한 선형 변환 국소 영역에서 비선형 변환을 선형 변환으로 근사 ### Jacobian Matrix Usages \|Title\| \|:-:\| > [Jacobian prerequisite knowledge (video) \| Khan Academy](https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/jacobian/v/jacobian-prerequisite-knowledge) > [자코비안(Jacobian) 행렬의 기하학적 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/07/24/Jacobian.html) > [Jacobian matrix and determinant](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)	3d36041b4bf64dcd96bd06ff680fe810
*Matrix Computation*	Matrix Usages	Jun 20, 2022	Alan Jo	Alan Jo	Apr 6, 2023	[AI Library](https://texonom.com/ai-library-30022d621bfd4843b908559bf1f6c1ac) [Machine Learning](https://texonom.com/machine-learning-96195e7f57d74bcf9e8719a53394e421)	### *Matrix Computation Library* \|Title\| \|:-:\| \|[bolt dbalock](https://texonom.com/bolt-dbalock-2596f1659f5748009f1f41e5050d23ef)\|	af84cd99a7d047caa70d3517e26f73e3
Matrix Derivative	Matrix Usages	Apr 17, 2023	Alan Jo	Alan Jo	Apr 17, 2023	[Transpose of Matrix](https://texonom.com/transpose-of-matrix-639bc5b5563c4c54b3e9ef0f37342bee)	행렬 크기 줄이는 방향으로, 안되면 transpose $$x^TB \rightarrow B \newlinex^Tb \rightarrow b \newlinex^Tx \rightarrow 2x \newlinex^TBx \rightarrow 2Bx \newliney^TBx \rightarrow B^Ty \newline$$ ### Matrix Derivative Usages \|Title\| \|:-:\| \|[Hessian Matrix](https://texonom.com/hessian-matrix-e1ebbf5284284a1793233973648ef0b6)\| > [Untitled](https://atmos.washington.edu/~dennis/MatrixCalculus.pdf) > [Untitled](http://www.gatsby.ucl.ac.uk/teaching/courses/sntn/sntn-2017/resources/Matrix_derivatives_cribsheet.pdf)	67e3bac465684331aa5205893b542749
Matrix Padding	Matrix Usages	Apr 6, 2023	Alan Jo	Alan Jo	Apr 6, 2023		### Normally Zero Padding which fills 0 주어진 행렬의 크기를 일정한 크기로 맞추기 위해 추가되는 값	0f44aaaee9d54bb3a6960130541ac90a
bolt dbalock	Matrix Computation Library	Jun 20, 2022	null	null	null	null	### 10x faster matrix and vector operations [bolt](https://github.com/dblalock/bolt)	2596f1659f5748009f1f41e5050d23ef
Hessian Matrix	null	null	null	null	null	null	### Math 어떤 함수의 2계 도함수들을 이용하여 행렬을 만든 것 그러므로 헤시안 행렬은 2차 미분계수와 비슷한 의미를 갖는다 $$H_{ij} = \frac{\partial^2l(\theta)}{\partial\theta_i\partial\theta_j}$$ ### Geometry 헤시안 행렬을 이용하면 특정 함수의 특정 위치가 위로 볼록한지, 아래로 볼록한지, 안장점인지를 판단할 수 있다는 의미 기본 bowl의 형태를 더 볼록하거나 오목하게 만드는 기하학적인 변환을 수행해주는 역할 > [헤세 행렬(Hessian Matrix)의 기하학적 의미](https://angeloyeo.github.io/2020/06/17/Hessian.html)	e1ebbf5284284a1793233973648ef0b6
Anisotropic	Vector Notion	May 18, 2023	Alan Jo	Alan Jo	Jul 10, 2023		이방성 주어진 공간에서 특정 방향으로만 향해 있어서 일종의 cone 형태를 이루고 있는 것 > [Contextual Embedding - How Contextual are Contextualized Word Representations?](https://velog.io/@stapers/Contextual-Embedding-How-Contextual-are-Contextualized-Word-Representations)	56427ad6cfc84d46a0b46606b25bb7bd
Isotropic	Vector Notion	May 18, 2023	Alan Jo	Alan Jo	Jul 10, 2023		등방성 방향과 상관없는 성질 벡터가 주어진 공간에서 모든 방향으로 존재하는 상황	13d450b4d2d24ef18af47546f578c3e7
Linear Independent	Vector Notion	Nov 5, 2019	Alan Jo	Seong-lae Cho	Sep 13, 2023	[Linearity](https://texonom.com/linearity-53be0991221249d794ed8047fe36ecb5)	### Linear Independent notion \|Title\| \|:-:\| \|[Orthogonality](https://texonom.com/orthogonality-d694f04a603d46f18da03a4dc737ca51)\| \|[Linear Dependent](https://texonom.com/linear-dependent-895c1bc53e2f48b494ef2e2837c16bbf)\| > [직교성(orthogonality)의 공학적 의미](https://satlab.tistory.com/37)	da490558cce24664be62d499d40b96a2
Unit Vector	Vector Notion	Oct 10, 2022	Alan Jo	Alan Jo	Apr 6, 2023		## Normalized Vector A unit vector is often denoted by a lowercase letter with a circumflex, or "hat" ### Unit Vectors \|Title\| \|:-:\| \|[Orthonormal Vectors](https://texonom.com/orthonormal-vectors-6c05c455048d4d729c7a86ad3802b339)\|	9d0e1e60888c4f338745830b40584981
Vector Operation	Vector Notion	Apr 6, 2023	Alan Jo	Alan Jo	Apr 6, 2023		### Vector Operations \|Title\| \|:-:\| \|[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)\| \|[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)\| \|[Vector Addition](https://texonom.com/vector-addition-e75327dc94934cbb895656ca08112007)\| \|[Vector Multiplication](https://texonom.com/vector-multiplication-aa46ebeebb3a4aa2bdd459a13dc655dd)\|	61d2aa5fe6594af7a30b45309946b2d7
Vector Space	null	null	null	null	null	null	a module over a field, which also carries a multiplication operation that is compatible with the module structure ### Vector Space Notion \|Title\| \|:-:\| \|[Subspace](https://texonom.com/subspace-e559a723195a4ae5bda391c3332695d6)\| \|[Basis Vector](https://texonom.com/basis-vector-374bc63669314745b4513e0ba77704d5)\| \|[Inner Product space](https://texonom.com/inner-product-space-47e25eabbade4a0f923601f5f58255b2)\|	7681a959944242619d201953076294f2
Orthonormal Vectors	null	null	null	null	null	null	반드시 한 쌍 이상의 벡터로부터 정의되어야 > [[Linear Algebra] Lecture 17-(1) 직교행렬(Orthogonal Matrices)과 그람 슈미트 과정(Gram-Schmidt Process)](https://twlab.tistory.com/37)	6c05c455048d4d729c7a86ad3802b339
Inner product	Vector Operations	Jan 23, 2022	Alan Jo	Alan Jo	Jun 11, 2023		## Dot Product 내적은 두 신호가 얼마나 닮았는냐를 계산해주는 일이기도 함 [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)	0362165a5a3d490784d9c3ff41b2b19f
Outer Product	Vector Operations	Jan 23, 2022	Alan Jo	Alan Jo	Apr 6, 2023		## Cross Product - Anti [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a) $$\vec{u} \times \vec{v} = - \vec{v} \times \vec{u}$$	4106750021e944d985d7fdb1b42570ae
Vector Addition	Vector Operations	Jan 23, 2022	Alan Jo	Alan Jo	Apr 6, 2023		move origin	e75327dc94934cbb895656ca08112007
Vector Multiplication	Vector Operations	Jan 23, 2022	Alan Jo	Alan Jo	Apr 6, 2023		### scaling scalars - change length scaler can be [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)	aa46ebeebb3a4aa2bdd459a13dc655dd
Basis Vector	Vector Space Notion	May 23, 2023	Alan Jo	Alan Jo	May 23, 2023			374bc63669314745b4513e0ba77704d5
Inner Product space	Vector Space Notion	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023			47e25eabbade4a0f923601f5f58255b2
Subspace	Vector Space Notion	May 23, 2023	Alan Jo	Alan Jo	May 23, 2023			e559a723195a4ae5bda391c3332695d6
Vector Equation	Vector Usages	Oct 31, 2022	Alan Jo	Alan Jo	Oct 31, 2022		### Vector Equations \|Title\| \|:-:\| \|[Vector Equation of a Plane](https://texonom.com/vector-equation-of-a-plane-1f3a37a903984921bf16acf5bc138678)\| \|[Vector Equation of a Line](https://texonom.com/vector-equation-of-a-line-40c9a0f52a944427a5c69456ca4b429c)\|	122ad1c33c514ad3b2c9cee4aac00521
Vector Similarity	Vector Usages	Apr 28, 2023	Alan Jo	Alan Jo	Jun 5, 2023	[Latent Space](https://texonom.com/latent-space-d67b6bdef18b4058bfbc3d25f87ec087)	## Vectorized Pairwise Similarity $$<a, b>$$ - [Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f) - [Euclidean Distance](https://texonom.com/euclidean-distance-0d3a8b5dc5e04ee595dc85365b2d3fd9) ### Pairwise similarity matrix result value ### Vector Similarities \|Title\| \|:-:\| \|[Cosine Similarity](https://texonom.com/cosine-similarity-0686a915d71749b6aecbe611fd0f3efd)\| ### Vector Similarity Algorithms \|Title\| \|:-:\| \|[HNSW Algorithm](https://texonom.com/hnsw-algorithm-2d387cef1103477f99d181e956f3d76d)\| \|[KNN Algorithm](https://texonom.com/knn-algorithm-3b5f079c416349f5af4a54537c873d4b)\| \|[Annoy Algorithm](https://texonom.com/annoy-algorithm-b91a06fdf7a64255a3f0452b28abd4df)\| ### Vector Similarity Tools \|Title\| \|:-:\| \|[Faiss](https://texonom.com/faiss-445af9045d9c486995f31a2e75cff3ba)\|	846675a408e74235acc836302110ab07
Vector Equation of a Line	Vector Equations	Oct 31, 2022	Alan Jo	Alan Jo	Oct 31, 2022		$$x = \vec{endpoint} + t \cdot\vec{direction}$$ if (t>0), it is ray if t has a range, it is segment ### distance between one straight line and one point $$D = \frac{\vec{AP} \times \vec{d}} {\vec{d}} = \overline{AP}sin{\theta} $$ ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fa06502d3-f475-42a8-9c24-b65400835101%2FUntitled.png?table=block&id=88cf7bf2-f7b0-418f-a07e-a8181bc2a73d&cache=v2) ### Distance between two lines $$\vec{a_1} + t\cdot\vec{b_1}\vec{a_2} + t\cdot\vec{b_2}d = \|\frac{(\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1}\times \vec{b_2}) } {\|\vec{b_1} \times \vec{b_2}\|}\|$$ > [Lesson Explainer: The Perpendicular Distance between Points and Straight Lines in Space \| Nagwa](https://www.nagwa.com/en/explainers/939127418581/) > [Shortest Distance Between Two Lines in 3D](https://www.youtube.com/watch?v=6vpXM1dskmY)	40c9a0f52a944427a5c69456ca4b429c
Vector Equation of a Plane	Vector Equations	Oct 31, 2022	Alan Jo	Alan Jo	Oct 31, 2022		$$\vec{normal} \cdot(\vec{x} - \vec{point}) = 0$$ > [Lesson Explainer: Equation of a Plane: Vector, Scalar, and General Forms \| Nagwa](https://www.nagwa.com/en/explainers/373101390857/)	1f3a37a903984921bf16acf5bc138678
Cosine Similarity	Vector Similarities	Mar 10, 2023	Alan Jo	Alan Jo	Jun 1, 2023		차원이 높아질수록 [Curse of dimensionality](https://texonom.com/curse-of-dimensionality-343455a61aa14779b6edf4c93464fac3) 때문에 거리파악은 의미가 적어진다 그래서 유사도 각도로 계산	0686a915d71749b6aecbe611fd0f3efd
Annoy Algorithm	Vector Similarity Algorithms	Jun 1, 2023	Alan Jo	Alan Jo	Jun 1, 2023		## Approximate Nearest Neighbors [annoy](https://github.com/spotify/annoy) - 근사해서 가까운 벡터 찾음 - 데이터 추가가 어렵다	b91a06fdf7a64255a3f0452b28abd4df
HNSW Algorithm	Vector Similarity Algorithms	Jun 1, 2023	Alan Jo	Alan Jo	Jul 13, 2023	[Small worlds Network](https://texonom.com/small-worlds-network-b779baa02bc846b5970d67d561d755c0)	## Hierarchical Navigable Small words ![https://forward.nhn.com/2022/sessions/42](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2981ffe8-e2f7-403e-9cb5-50718e3bc8c4%2FUntitled.png?table=block&id=612850c1-5f74-400f-864c-92e75bd01de4&cache=v2) ### HNSW Algorithm Notion \|Title\| \|:-:\| \|[Probability Based Skip List](https://texonom.com/probability-based-skip-list-9111e1422511456bbfb7e7c3fa227860)\| ### HNSW Algorithm Tools \|Title\| \|:-:\| \|[HNSWlib](https://texonom.com/hnswlib-11dcfb3c5e5d448da1b0c7be3998520e)\| \|[](https://texonom.com/b47fdad5d11f4717974fc3aac3d667bd)\| > [대충? 거의 정확하다! 벡터 검색 엔진에 ANN HNSW 알고리즘 도입기 (feat. SWIG Golang)](https://forward.nhn.com/2022/sessions/42)	2d387cef1103477f99d181e956f3d76d
KNN Algorithm	Vector Similarity Algorithms	Jun 1, 2023	Alan Jo	Alan Jo	Jun 1, 2023			3b5f079c416349f5af4a54537c873d4b
Probability Based Skip List	HNSW Algorithm Notion	Jun 1, 2023	Alan Jo	Alan Jo	Jun 1, 2023		![https://forward.nhn.com/2022/sessions/42](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F9274bee0-ec54-41d1-9bbb-53d66cb16311%2FUntitled.png?table=block&id=7014159d-9f00-4e50-8211-65fc8d4f0d39&cache=v2)	9111e1422511456bbfb7e7c3fa227860
[pg_embedding](https://github.com/neondatabase/pg_embedding)	HNSW Algorithm Tools	Jun 1, 2023	Alan Jo	Alan Jo	Jul 13, 2023			b47fdad5d11f4717974fc3aac3d667bd
HNSWlib	HNSW Algorithm Tools	Jun 1, 2023	Alan Jo	Alan Jo	Jun 1, 2023		### HNSWlib Usages \|Title\| \|:-:\| \|[](https://texonom.com/2ab069bd60b3423faa91c460afa92955)\| \|[hnswlib python](https://texonom.com/hnswlib-python-8b119e7305e74014b4761b8c40404767)\|	11dcfb3c5e5d448da1b0c7be3998520e
[hnswlib-node](https://github.com/yoshoku/hnswlib-node)	HNSWlib Usages	Jun 1, 2023	Alan Jo	Alan Jo	Jun 1, 2023			2ab069bd60b3423faa91c460afa92955
hnswlib python	HNSWlib Usages	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023		[hnswlib](https://github.com/nmslib/hnswlib) ### Index space > [How to use the hnswlib.Index function in hnswlib \| Snyk](https://snyk.io/advisor/python/hnswlib/functions/hnswlib.Index)	8b119e7305e74014b4761b8c40404767
Faiss	Vector Similarity Tools	Mar 10, 2023	Alan Jo	Alan Jo	Apr 28, 2023		> [Faiss 시작하기](https://velog.io/@nawnoes/Faiss-시작하기)	445af9045d9c486995f31a2e75cff3ba
BLAS	Linear Algebra Usages	Feb 21, 2022	Alan Jo	Alan Jo	Jun 5, 2023		## Basic Linear Algebra Subprograms [nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c) > [세상을 바꾼 10개의 컴퓨터 코드 - Sciencetimes](https://www.sciencetimes.co.kr/news/%ec%84%b8%ec%83%81%ec%9d%84-%eb%b0%94%ea%be%bc-10%ea%b0%9c%ec%9d%98-%ec%bb%b4%ed%93%a8%ed%84%b0-%ec%bd%94%eb%93%9c/)	17d8d7491b2147829b88426574733651
Vectorious	Linear Algebra Usages	Jun 5, 2023	Alan Jo	Alan Jo	Jun 5, 2023		[vectorious](https://github.com/mateogianolio/vectorious) Node js [N-API](https://texonom.com/n-api-8f1b5ef6b76847deb6e7dd2c688b82fd) [nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c)	fd5a587523a9423089cf74ae0899b8ce
nblas	BLAS	null	null	null	null	null		e7eb59d9195848f78ee8e73cd23e916c
Arithmetic Precision	Arithmetic Notion	Dec 17, 2021	Alan Jo	Alan Jo	Jun 6, 2023		정밀도 산술 ### Highest-order operand	baffc5389f06430eb20806e985685c9b
Elementary arithmetic	null	null	null	null	null	null		57a9f00b3f30433299816f32b4d49fbd
Fixed-point arithmetic	Arithmetic Notion	Dec 17, 2021	Alan Jo	Alan Jo	Jun 6, 2023		> [Fixed-point arithmetic - Wikipedia](https://en.wikipedia.org/wiki/Fixed-point_arithmetic)	c46e0722c58c4e2fbc1d2f7027bf6fbe
The Tower Function	Calculus Examples	Aug 23, 2020	Alan Jo	Alan Jo	Aug 29, 2021		> [밑이 무한히 계속 생기는 함수 2탄 \| The Power Tower Function](https://www.youtube.com/watch?v=doItxhmZavo) > [역사상 최고의 수학자도 알 수 없었던 함수 #Shorts](https://www.youtube.com/watch?v=GPe9Lt8OAdM)	7a63cab2617a402782fbf88c9055d43c
Concave Point	Calculus Notion	Mar 9, 2023	Alan Jo	Alan Jo	Mar 9, 2023			c3f6835eb9ef4378830d3b916da3f074
Convex Point	Calculus Notion	Mar 9, 2023	Alan Jo	Alan Jo	Mar 9, 2023			160b14cc61114a8a9be9797578e11c7a
Derivation	Calculus Notion	Aug 29, 2021	Alan Jo	Alan Jo	Jun 11, 2023	[Vector Field](https://texonom.com/vector-field-ff7ea488edb74510a51e844eee7a222f) [Scalar Field](https://texonom.com/scalar-field-a0e05a5b310c4a6283bc214ec02383e0)	## Differentiation ### Derivation Notion \|Title\| \|:-:\| \|[Differential Equation](https://texonom.com/differential-equation-419a4e3d42924ec79afc700734b88996)\| \|[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb)\| \|[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)\| \|[Divergence](https://texonom.com/divergence-d8b434d51ae549db839bf075fa2452bb)\| \|[Curl](https://texonom.com/curl-5472397a80234ddeb5d8dca28b9ccae2)\| \|[Del](https://texonom.com/del-f6d1cdf554914c98a06c1180179bf401)\| \|[Antiderivative](https://texonom.com/antiderivative-7e0e92c4cdcb4bc48c323100aa512c81)\| > [Gradient, Divergence, Curl에 대하여.](https://sillurian.tistory.com/10)	79d0547aee0d45ce93cdae0f26bc3ce6
Explicit Function	Calculus Notion	Nov 14, 2022	Alan Jo	Alan Jo	Mar 9, 2023		### 양함수 종속변수와 독립변수들이 분리된 함수	df8104e2876c42e9b112f6308718e3bc
Implicit Function	Calculus Notion	Nov 14, 2022	Alan Jo	Alan Jo	Dec 5, 2022	[Normal Vector](https://texonom.com/normal-vector-84412bdb0b8c43e3a206cd54bc9901f7)	### 음함수 종속변수가 독립변수와 분리되지 않은 하나의 관계식 ### Implicit Function Notion \|Title\| \|:-:\| \|[Implicit Function Theorem](https://texonom.com/implicit-function-theorem-37a2205114464b178be0937046505686)\|	1e383ff61a8b4831abca72e4c37649bd
Inflection point	Calculus Notion	Jan 11, 2022	Alan Jo	Alan Jo	Jan 11, 2022		변곡점	6448287d912942cea85ee85a981505d6
Integral	Calculus Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 5, 2022		### Integral Notion \|Title\| \|:-:\| \|[Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)\| \|[Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)\|	ed91b8e9d33d49bfa6a32e93f7bfdfca
Local extremum point	null	null	null	null	null	null		f7a7579a29474436b2a8670a28fed921
Vector Calculus	Calculus Notion	Oct 30, 2022	Alan Jo	Alan Jo	Oct 30, 2022	[Vector](https://texonom.com/vector-9ed4d1c8519c496dbfadb1f6b3522255)	### Vector Calculus Notion \|Title\| \|:-:\| \|[Vector Differential Operator](https://texonom.com/vector-differential-operator-4f2b33fb3ea348ba978e3d117c8246a4)\| \|[Vector Integral Theorem](https://texonom.com/vector-integral-theorem-2295053d5673460a927e2479d83070b8)\| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)	77976c6127ad49c9a6611e16a40f337f
Curl	Derivation Notion	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023	[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)	Derivative which map Vector field to Vector field ### describes the infinitesimal circulation of a vector field ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fd5c23481-3bb4-4f34-ac18-532b99d81275%2FUntitled.png?table=block&id=53692b35-0349-441c-a6e1-a344c3881ca4&cache=v2) ### Curl Notion \|Title\| \|:-:\| \|[Stokes' theorem](https://texonom.com/stokes-theorem-d3b508adeddc45c98a0f27d792b17999)\| > [Curl (mathematics)](https://en.wikipedia.org/wiki/Curl_(mathematics))	5472397a80234ddeb5d8dca28b9ccae2
Del	Derivation Notion	May 6, 2023	Alan Jo	Alan Jo	Jun 11, 2023		Del operator nabla symbol $$\nabla$$	f6d1cdf554914c98a06c1180179bf401
Derivative	Derivation Notion	Oct 30, 2022	Alan Jo	Alan Jo	May 6, 2023	[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)	### Derivative Notion \|Title\| \|:-:\| \|[Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)\| \|[Chain Rule](https://texonom.com/chain-rule-cdc4287f5b2a4bcda97886907836d5d0)\| \|[Quotient Rule](https://texonom.com/quotient-rule-283d6806817f4684838f842865de0397)\|	67f45809e7a84277be4fca74a3b86ceb
Differential Equation	Derivation Notion	Aug 29, 2021	Alan Jo	Alan Jo	Jun 15, 2022		### Differential Equation Notion \|Title\| \|:-:\| ### Differential Equation Methods \|Title\| \|:-:\| \|[Laplace Transform](https://texonom.com/laplace-transform-155ade7fe1bc4712b183339c25d68fda)\|	419a4e3d42924ec79afc700734b88996
Divergence	Derivation Notion	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023	[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)	## Vector field to multi variable scalar function ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5f8b43e7-da4b-427a-accd-e85df5fa9ddc%2FUntitled.png?table=block&id=1f1ae617-32ae-4409-9db9-ada1dc25261d&cache=v2) ### Divergence Notion \|Title\| \|:-:\| \|[Gauss Divergence Theorem](https://texonom.com/gauss-divergence-theorem-6b5f20e56c78488997efddf7f1fd2ebf)\| > [Divergence](https://en.wikipedia.org/wiki/Divergence)	d8b434d51ae549db839bf075fa2452bb
Gradient	Derivation Notion	Mar 16, 2023	Alan Jo	Alan Jo	Jun 11, 2023		### Derivate multi variable scalar function to vector field using [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9) ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F78130f9f-bc29-4ee5-9b29-6a32246a0d4d%2FUntitled.png?table=block&id=246a18b6-2d4a-4f04-bd4e-a5e6c984fd37&cache=v2) 2차일 때 등고선 개념으로 이해하면 쉽다. 그래디언트의 크기는 경사도 > [Gradient, Divergence, Curl에 대하여.](https://sillurian.tistory.com/10) > [수학 - Divergence ,Gradient, Curl[미완]](https://m.blog.naver.com/ptm0228/221676279348) > [Gradient](https://en.wikipedia.org/wiki/Gradient)	685dfab242a4421da9f5bd89ae5975ed
Stokes' theorem	Curl Notion	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023			d3b508adeddc45c98a0f27d792b17999
Chain Rule	null	null	null	null	null	null	> [Chain rule](https://en.wikipedia.org/wiki/Chain_rule)	cdc4287f5b2a4bcda97886907836d5d0
Partial Derivative	Derivative Notion	Oct 30, 2022	Alan Jo	Alan Jo	May 6, 2023	[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)	다변수 함수의 특정 변수를 제외한 나머지 변수를 상수로 간주하여 미분하는 것 Nabla와 혼용하지 않기 ### partial f partial x $$\frac{\partial f}{\partial x}$$ $$\lim_{h\rightarrow 0}\frac{f(x +h,y) - f(x,y)} {x + h - x}$$ ### Partial Derivative Notion \|Title\| \|:-:\|	e9c7ff432f1c43af8669ef0addd78cd9
Quotient Rule	Derivative Notion	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023			283d6806817f4684838f842865de0397
Laplace Transform	Differential Equation Methods	Jun 15, 2022	Alan Jo	Alan Jo	Sep 13, 2023	[Pierre-Simon Laplace](https://texonom.com/pierre-simonlaplace-9a48a934756544579f8398d8a349029b)	ln으로 처리하고 미분방정식 처리에 용이하다 발산하는 함수에 대한 [Fourier Transform](https://texonom.com/fourier-transform-5ee1f9063a9743dd9846ddc600286d5a)을 적용하기 위한 방법 ### Laplace Transform Notion \|Title\| \|:-:\| > [7분만에 이해해보는 라플라스 변환](https://www.youtube.com/watch?v=4ONICadjLBY)	155ade7fe1bc4712b183339c25d68fda
**Gauss Divergence Theorem**	Divergence Notion	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023	[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f) [Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)	> [Divergence theorem](https://en.wikipedia.org/wiki/Divergence_theorem) > [Gauss Divergence Theorem. Get the DEEPEST Intuition.](https://www.youtube.com/watch?v=zZqxbwl3Dno)	6b5f20e56c78488997efddf7f1fd2ebf
Implicit Function Theorem	Implicit Function Notion	Nov 14, 2022	Alan Jo	Alan Jo	Nov 14, 2022		> [Implicit function theorem - Wikipedia](https://en.wikipedia.org/wiki/Implicit_function_theorem)	37a2205114464b178be0937046505686
Lebesgue integral	Integral Notion	Apr 5, 2022	Alan Jo	Alan Jo	Jun 11, 2023	[Measure Theory](https://texonom.com/measure-theory-4fb6210801ea4d7abcb937cd068ba461) [Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)	### 르베그 적분 일반적인 측도 공간 위에 정의될 수 있는 적분 실수선 위에서의 르베그 적분은 리만 적분보다 더 일반적 리만 적분이 정의되지 않아도 르베그 적분이 정의되는 함수들이 존재 ### Lebesgue integrals \|Title\| \|:-:\| \|[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f)\| \|[Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)\| > [르베그 적분 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EB%A5%B4%EB%B2%A0%EA%B7%B8_%EC%A0%81%EB%B6%84)	df7652d80314427db614b002c7a74de0
Riemann integral	Integral Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 15, 2023	[Bernhard Riemann](https://texonom.com/bernhard-riemann-166d61214be5439ca5f7ba1090063a3e) [Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)	닫힌구간에 정의된 실숫값 함수의 적분의 종류 정의역 구간을 잘게 나눠, 각각의 작은 구간 위의 넓이를 직사각형의 넓이를 통해 근사	47f26748e1174265ae26d8a12b04fdca
Surface Integral	Lebesgue integrals	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023			29bad5fdca49449bb4a96603905b160f
**Volume integral**	Lebesgue integrals	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023			41bc72e8ff194d54b11f16135b751348
Vector Differential Operator	Vector Calculus Notion	Oct 30, 2022	Alan Jo	Alan Jo	Oct 30, 2022	[Derivation](https://texonom.com/derivation-79d0547aee0d45ce93cdae0f26bc3ce6)	### Vector Differential Operators \|Title\| \|:-:\| \|[Vector Curl](https://texonom.com/vector-curl-17571a486321485e80a305ac4bb93e19)\| \|[Gradient Vector](https://texonom.com/gradient-vector-d3940976683946f89bd512d0bbf45672)\| \|[Vector Divergence](https://texonom.com/vector-divergence-0ee28e695ecd48a68665f8a30cb7c864)\| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)	4f2b33fb3ea348ba978e3d117c8246a4
Vector Integral Theorem	Vector Calculus Notion	Oct 30, 2022	Alan Jo	Alan Jo	Oct 30, 2022		### Vector Integral Theorems \|Title\| \|:-:\| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)	2295053d5673460a927e2479d83070b8
Gradient Vector	Vector Differential Operators	Oct 30, 2022	Alan Jo	Alan Jo	Oct 7, 2022	[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb) [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)	$$\vec{z}, \vec{x} \text{ } is \text{ } \text{ on the surface } f(\vec{x}) = 0$$ $$\vec{z} = \vec{x} + \epsilon\vec{u} $$ $$f(z) = f(x + \epsilon u) - f(x_1 + \epsilon u_1, x_2 + \epsilon u_2, x_3 + \epsilon u_3)$$ $$h(x, y, z) = 0$$ $$\nabla h = (\frac{dh}{dx}, \frac{dh}{dy}, \frac{dh}{dz})$$ 심플하게 편미분으로 구해도 되고 $$\nabla h = \frac{d\vec{h}}{dx} \times \frac{d\vec{h}}{dy}$$ xy 아니더라도 곡면의 해당 접평면상에서 움직이는 거라 yz나 xz 도 가능 > [Untitled](https://www.cs.ucr.edu/~craigs/courses/2022-fall-cs-130/lectures/normals.pdf)	d3940976683946f89bd512d0bbf45672
Vector Curl	Vector Differential Operators	Oct 30, 2022	Alan Jo	Alan Jo	Oct 30, 2022		회전 Operator 3차원 벡터장을 다른 3차원 벡터장으로 대응시키는 1차 미분 연산자의 하나	17571a486321485e80a305ac4bb93e19
Vector Divergence	Vector Differential Operators	Oct 30, 2022	Alan Jo	Alan Jo	Oct 30, 2022			0ee28e695ecd48a68665f8a30cb7c864
Butterfly Effect	Chaos Theory Notion	Jun 22, 2021	null	null	null			62e1b65850da4b3ab2d429292473f8a1
Complex System	Chaos Theory Notion	May 16, 2022	null	null	null		> [Complex system - Wikipedia](https://en.wikipedia.org/wiki/Complex_system)	b2457d8f6fcc4fe2abffd71828908a1f
Lorenz Attractor	Chaos Theory Notion	Jun 22, 2021	null	null	null			b3249a819200420797f82e204cc9d58c
Combinatorics	Discrete Math Topics	May 13, 2023	Alan Jo	Alan Jo	May 13, 2023			887b47c6bb1c46388a8387d89bd304cf
Order Theory	Discrete Math Topics	May 13, 2023	Alan Jo	Alan Jo	May 13, 2023			8c7e8fb9638f41b19b6829d686fc6f9b
Pigeonhole principle	Discrete Math Topics	Nov 5, 2019	Alan Jo	Seong-lae Cho	May 13, 2023		비둘기집 원리	998c7a67c04e43d28b132eaa02d5f0d8
Graph Signal Processing	Graph Theory Fields	Apr 28, 2023	Alan Jo	Alan Jo	Apr 28, 2023		## GSP > [Untitled](https://web.media.mit.edu/~xdong/talk/BDI_GSP.pdf)	a6551be225984e4cad9bdd244d6a58b5
Dynamical System	Ergodic theory Notion	Apr 3, 2022	Alan Jo	Alan Jo	Aug 28, 2023		### Dynamical System Notion \|Title\| \|:-:\| \|[Dynamical systems theory](https://texonom.com/dynamical-systems-theory-b693764c797945f1b330d386a85ad936)\| \|[Logistic Map](https://texonom.com/logistic-map-d968681610c749e9983e28f97ee5c50b)\| > [Dynamical system - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_system)	a4e33185067b49b28e8f62454028f7b1
Poincare Recurrence Theorem	Ergodic theory Notion	Nov 13, 2019	Alan Jo	Alan Jo	Jul 12, 2023	[Grigori Perelman](https://texonom.com/grigori-perelman-c53487e421c94fceb6a83431c7cc1149) [Henri Poincare](https://texonom.com/henri-poincare-1382da083d864065972f27c140c4aa64)	### 푸앵카레 재귀 정리 특정한 계는 충분한 시간이 지난 후에는 초기상태와 아주 가까운 상태로 회귀한다는 내용의 정리 에너지 준위가 이산적인 양자역학적 계에 대해서도 비슷한 정리가 성립 > [Poincaré recurrence theorem - Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem)	1aca4c4a3d2446c1892de56b1071953c
Dynamical systems theory	Dynamical System Notion	Apr 3, 2022	Alan Jo	Alan Jo	Apr 3, 2022		> [Dynamical systems theory - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_systems_theory)	b693764c797945f1b330d386a85ad936
Category Theory	null	null	null	null	null	null	집합론의 반대에 해당하는 개념 요소 대신 요소들 간의 관계에 주목하여 추상적인 개념들을 다루고자 하는 수학 이론 ### Category Theory Notion \|Title\| \|:-:\| \|[Topos Theroy](https://texonom.com/topos-theroy-cd8c3fed6bb14e8cbda9294ed472a4df)\| > [Category theory](https://en.wikipedia.org/wiki/Category_theory)	1b6594b7d4ce4c128ec2f9aed95d9f3c
Gödel’s incompleteness theorem	Foundations of Mathematics Notion	May 30, 2021	Alan Jo	Alan Jo	Sep 17, 2023		1차 논리에서 증명 가능한 명제의 집합은 모형을 갖는다는 정리 수리논리학 즉, 증명 이론으로 정의한 진리와 모형 이론으로 정의한 진리가 서로 일치 을 피하기 위해 아무리 세심하게 공리계를 설계해도 그것을 피할 수는 없다는 것을 증명하였으며, 이것이 불완전성 정리 [2nd Gödel’s incompleteness theorem](https://texonom.com/2nd-gdels-incompleteness-theorem-173d1bd5bdac42448e637253f602a763) > [Zarathu Blog: 괴델의 불완전성 정리](https://blog.zarathu.com/posts/2019-05-20-godelincompleteness/) > [괴델의 불완전성 정리](https://jinseob2kim.github.io/godel.html) > [괴델의 완전성 정리 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EA%B4%B4%EB%8D%B8%EC%9D%98_%EC%99%84%EC%A0%84%EC%84%B1_%EC%A0%95%EB%A6%AC) > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw)	820d082fd9bf424f8125dda3bf9e859b
Langlands program	Foundations of Mathematics Notion	Aug 25, 2022	Alan Jo	Alan Jo	Aug 25, 2022	[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2) [Harmonic Analysis](https://texonom.com/harmonic-analysis-e1e54ebeffd0407088bebab57acbfd53)	대수적 수 이론에서 갈루아 군들을 보형 형식에 관련시키고 국소체와 아델 환에 대한 대수적 그룹의 표현 이론을 서로 연관짓는 광범위한 영향력 있는 추측의 망 로버트 랭글랜즈에 의해 제안 > [The Biggest Project in Modern Mathematics](https://youtu.be/_bJeKUosqoY)	629d720ec59b4bf4a42c0b066675b220
Set Theory	null	null	null	null	null	null	### Set Theory Notion \|Title\| \|:-:\| \|[Russell's paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)\| \|[Infinite Set](https://texonom.com/infinite-set-971d3736190a4752a1ee3d1e2fea7028)\| \|[Cantor's theorem](https://texonom.com/cantors-theorem-3057f62f2b4947448aaf1c7a0fd8904d)\| \|[Power Set](https://texonom.com/power-set-58038c26c9ef49e1bf59cae859c90394)\| \|[Continuum Hypothesis](https://texonom.com/continuum-hypothesis-8792f326812a41d0b546db08fbd82a52)\| \|[Diagonal Argument](https://texonom.com/diagonal-argument-8a8921d2ba3745a199517d8650d50395)\| \|[Countable Set](https://texonom.com/countable-set-94c63f44bb5c4334857afe94d13cad59)\| \|[Uncountable Set](https://texonom.com/uncountable-set-287e751cba3c466e92f123ca2f04e13f)\| \|[Infinite Set](https://texonom.com/infinite-set-93755bd42acf41e2ac688467ad687885)\| \|[Finite Set](https://texonom.com/finite-set-63ed2bdb689946429effb738e5422255)\| \|[Cantor’s paradox](https://texonom.com/cantors-paradox-c84022d0e5e344889da73daf136602ce)\| \|[Naive set theory](https://texonom.com/naive-set-theory-67e68d75439f41bb8eb032834706044d)\| \|[Equinumerosity](https://texonom.com/equinumerosity-907dd17f4fab4b9b8212011bc680e5bf)\| \|[Cantor set](https://texonom.com/cantor-set-9cfdfcff7f82497eaca09074d723a722)\| \|[Complement Set](https://texonom.com/complement-set-2ed91c78263a44a18c5a65ab86be77db)\| \|[Symmetric difference](https://texonom.com/symmetric-difference-07bdea8546c04dabb5cd4ec7fd61b67b)\| \|[Poset](https://texonom.com/poset-9a126737d3414bfc9225fe391603b9ad)\| \|[Borel set](https://texonom.com/borel-set-76ba23edebd64061af05154588ab2870)\| \|[ZFC](https://texonom.com/zfc-f844451d3f134288a92febc7b8e8257b)\| > [Untitled](https://www.math.snu.ac.kr/~kye/lecture/02_1_set_theory/%BE%E7%C0%BA%C7%FD.htm) ### Set > [MySQL 합집합, 교집합, 차집합, 대칭차](https://zetawiki.com/wiki/MySQL_%ED%95%A9%EC%A7%91%ED%95%A9,_%EA%B5%90%EC%A7%91%ED%95%A9,_%EC%B0%A8%EC%A7%91%ED%95%A9,_%EB%8C%80%EC%B9%AD%EC%B0%A8)	a74b3919af5e4e6e885862f6f76103f9
Type Theory	Foundations of Mathematics Notion	May 13, 2023	Alan Jo	Alan Jo	May 13, 2023			a6967220456b47498b951f11598381f7
Topos Theroy	Category Theory Notion	Jul 12, 2023	Alan Jo	Alan Jo	Jul 12, 2023		### Topos Theroy Notion \|Title\| \|:-:\| \|[Topos](https://texonom.com/topos-6d05bbca3e3d4051bc512027cb7543ef)\| \|[Elementary Topoi](https://texonom.com/elementary-topoi-99bdc34b5e4a47e3b3597391ceb5ea7a)\| \|[Grothendieck tp[po](https://texonom.com/grothendieck-tppo-76ca3dfbb8b644648d81fd583eefbf28)\| > [Topos](https://en.wikipedia.org/wiki/Topos)	cd8c3fed6bb14e8cbda9294ed472a4df
Elementary Topoi	Topos Theroy Notion	Jul 12, 2023	Alan Jo	Alan Jo	Jul 12, 2023	[Logic](https://texonom.com/logic-e562053ace984677a72cb9eaf5c6f91e)		99bdc34b5e4a47e3b3597391ceb5ea7a
Grothendieck tp[po	Topos Theroy Notion	Jul 12, 2023	Alan Jo	Alan Jo	Jul 12, 2023	[Algebraic Geometry](https://texonom.com/algebraic-geometry-4dc98f1cbfff43e1b969e0b660c484c2)		76ca3dfbb8b644648d81fd583eefbf28
Topos	Topos Theroy Notion	Jul 12, 2023	Alan Jo	Alan Jo	Jul 12, 2023	[Sheaf](https://texonom.com/sheaf-c1aa0624425d40ab86351c509a86b389)	### 일반화된 공간 개념들을 일반화시켜서 다루는 것	6d05bbca3e3d4051bc512027cb7543ef
2nd Gödel’s incompleteness theorem	Gödel’s incompleteness theorem	null	null	null	null	null	> [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw)	173d1bd5bdac42448e637253f602a763
Borel set	Set Theory Notion	Mar 27, 2023	Alan Jo	Alan Jo	Mar 27, 2023			76ba23edebd64061af05154588ab2870
Cantor set	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 15, 2023		### 비가산 무한집합 실수에서 닫힌 구간 \left[0, 1 \right] [0,1]를 3등분해나가면서 가운데 것을 제거하는 작업을 반복하여 얻는 집합 비가산 집합임에도 측도가 0인 집합 즉 길이가 0이다 프랙털의 일종 0과 1사이의 실루로 이루어진 집합이고 3등분해서 가운데 구간을 반복적으로 제외하는 방식으로 만든다 조밀한 곳이 없는 완전집합 [Cantor function](https://texonom.com/cantor-function-bab4b944c0cb44bdb0089d40ec6b1542) > [Cantor set - Wikipedia](https://en.wikipedia.org/wiki/Cantor_set)	9cfdfcff7f82497eaca09074d723a722
Cantor’s paradox	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 5, 2022	[Russell's paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)	모든 집합들의 모임이 집합을 이룰 수 없다	c84022d0e5e344889da73daf136602ce
Cantor's theorem	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 5, 2022		멱집합의 크기가 항상 원래의 집합의 크기보다 크다는 정리 즉 집합과 멱집합의 원소는 일대일 대응할 수 없다 > [칸토어의 정리 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EC%B9%B8%ED%86%A0%EC%96%B4%EC%9D%98_%EC%A0%95%EB%A6%AC)	3057f62f2b4947448aaf1c7a0fd8904d
Complement Set	Set Theory Notion	Oct 31, 2022	Alan Jo	Alan Jo	Oct 31, 2022			2ed91c78263a44a18c5a65ab86be77db
Continuum Hypothesis	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 5, 2022		연속체 가설 표준적 공리계로는 증명할 수도, 반증할 수도 없다 실수 집합의 모든 부분 집합은 가산집합이거나 아니면 실수 집합과 크기가 같다는 명제 힐베르트 문제의 1번	8792f326812a41d0b546db08fbd82a52
Countable Set	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 15, 2023		### 가산집합 자연수 정수는 가산이고 유리수도 가산인데 실수는 비가산	94c63f44bb5c4334857afe94d13cad59
Diagonal Argument	Set Theory Notion	Apr 5, 2022	Alan Jo	Alan Jo	Apr 5, 2022		칸토어가 실수가 자연수보다 많음을 증명하는 데 사용한 방법 실수 집합이 비가산집합임을 보이는 데 사용된다 > [대각선 논법 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EB%8C%80%EA%B0%81%EC%84%A0_%EB%85%BC%EB%B2%95)	8a8921d2ba3745a199517d8650d50395

Jacobian Matrix

Matrix Usages

Jun 2, 2023

Alan Jo

Jun 2, 2023

행렬의 원소들은 모두 1차 미분 계수로 구성 즉 미소 변화에 관한 선형 변환 국소 영역에서 **비선형 변환을 선형 변환으로 근사** ### Jacobian Matrix Usages |Title| |:-:| > [Jacobian prerequisite knowledge (video) | Khan Academy](https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/jacobian/v/jacobian-prerequisite-knowledge) > [자코비안(Jacobian) 행렬의 기하학적 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/07/24/Jacobian.html) > [Jacobian matrix and determinant](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)

3d36041b4bf64dcd96bd06ff680fe810

***Matrix Computation***

Matrix Usages

Jun 20, 2022

Alan Jo

Apr 6, 2023

[AI Library](https://texonom.com/ai-library-30022d621bfd4843b908559bf1f6c1ac) [Machine Learning](https://texonom.com/machine-learning-96195e7f57d74bcf9e8719a53394e421)

af84cd99a7d047caa70d3517e26f73e3

Matrix Derivative

Matrix Usages

Apr 17, 2023

Alan Jo

Apr 17, 2023

[Transpose of Matrix](https://texonom.com/transpose-of-matrix-639bc5b5563c4c54b3e9ef0f37342bee)

행렬 크기 줄이는 방향으로, 안되면 transpose $$x^TB \rightarrow B \newlinex^Tb \rightarrow b \newlinex^Tx \rightarrow 2x \newlinex^TBx \rightarrow 2Bx \newliney^TBx \rightarrow B^Ty \newline$$ ### Matrix Derivative Usages |Title| |:-:| |[Hessian Matrix](https://texonom.com/hessian-matrix-e1ebbf5284284a1793233973648ef0b6)| > [Untitled](https://atmos.washington.edu/~dennis/MatrixCalculus.pdf) > [Untitled](http://www.gatsby.ucl.ac.uk/teaching/courses/sntn/sntn-2017/resources/Matrix_derivatives_cribsheet.pdf)

67e3bac465684331aa5205893b542749

Matrix Padding

Matrix Usages

Apr 6, 2023

Alan Jo

Apr 6, 2023

### Normally Zero Padding which fills 0 주어진 행렬의 크기를 일정한 크기로 맞추기 위해 추가되는 값

0f44aaaee9d54bb3a6960130541ac90a

bolt dbalock

Matrix Computation Library

Jun 20, 2022

null

### 10x faster matrix and vector operations [bolt](https://github.com/dblalock/bolt)

2596f1659f5748009f1f41e5050d23ef

**Hessian Matrix**

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### Math 어떤 함수의 2계 도함수들을 이용하여 행렬을 만든 것 그러므로 **헤시안 행렬은 2차 미분계수와 비슷한 의미를 갖는다** $$H_{ij} = \frac{\partial^2l(\theta)}{\partial\theta_i\partial\theta_j}$$ ### Geometry 헤시안 행렬을 이용하면 특정 함수의 특정 위치가 위로 볼록한지, 아래로 볼록한지, 안장점인지를 판단할 수 있다는 의미 기본 bowl의 형태를 더 볼록하거나 오목하게 만드는 기하학적인 변환을 수행해주는 역할 > [헤세 행렬(Hessian Matrix)의 기하학적 의미](https://angeloyeo.github.io/2020/06/17/Hessian.html)

e1ebbf5284284a1793233973648ef0b6

Anisotropic

Vector Notion

May 18, 2023

Alan Jo

Jul 10, 2023

이방성 주어진 공간에서 특정 방향으로만 향해 있어서 일종의 cone 형태를 이루고 있는 것 > [Contextual Embedding - How Contextual are Contextualized Word Representations?](https://velog.io/@stapers/Contextual-Embedding-How-Contextual-are-Contextualized-Word-Representations)

56427ad6cfc84d46a0b46606b25bb7bd

Isotropic

Vector Notion

May 18, 2023

Alan Jo

Jul 10, 2023

**등방성** 방향과 상관없는 성질 벡터가 주어진 공간에서 모든 방향으로 존재하는 상황

13d450b4d2d24ef18af47546f578c3e7

Linear Independent

Vector Notion

Nov 5, 2019

Alan Jo

Seong-lae Cho

Sep 13, 2023

[Linearity](https://texonom.com/linearity-53be0991221249d794ed8047fe36ecb5)

### Linear Independent notion |Title| |:-:| |[Orthogonality](https://texonom.com/orthogonality-d694f04a603d46f18da03a4dc737ca51)| |[Linear Dependent](https://texonom.com/linear-dependent-895c1bc53e2f48b494ef2e2837c16bbf)| > [직교성(orthogonality)의 공학적 의미](https://satlab.tistory.com/37)

da490558cce24664be62d499d40b96a2

Unit Vector

Vector Notion

Oct 10, 2022

Alan Jo

Apr 6, 2023

## Normalized Vector **A unit vector** is often denoted by a lowercase letter with a circumflex, or "hat" ### Unit Vectors |Title| |:-:| |[Orthonormal Vectors](https://texonom.com/orthonormal-vectors-6c05c455048d4d729c7a86ad3802b339)|

9d0e1e60888c4f338745830b40584981

Vector Operation

Vector Notion

Apr 6, 2023

Alan Jo

Apr 6, 2023

### Vector Operations |Title| |:-:| |[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)| |[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)| |[Vector Addition](https://texonom.com/vector-addition-e75327dc94934cbb895656ca08112007)| |[Vector Multiplication](https://texonom.com/vector-multiplication-aa46ebeebb3a4aa2bdd459a13dc655dd)|

61d2aa5fe6594af7a30b45309946b2d7

Vector Space

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a module over a field, which also carries a multiplication operation that is compatible with the module structure ### Vector Space Notion |Title| |:-:| |[Subspace](https://texonom.com/subspace-e559a723195a4ae5bda391c3332695d6)| |[Basis Vector](https://texonom.com/basis-vector-374bc63669314745b4513e0ba77704d5)| |[Inner Product space](https://texonom.com/inner-product-space-47e25eabbade4a0f923601f5f58255b2)|

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Orthonormal Vectors

null

반드시 **한 쌍 이상의 벡터로부터 정의되어야** > [[Linear Algebra] Lecture 17-(1) 직교행렬(Orthogonal Matrices)과 그람 슈미트 과정(Gram-Schmidt Process)](https://twlab.tistory.com/37)

6c05c455048d4d729c7a86ad3802b339

Inner product

Vector Operations

Jan 23, 2022

Alan Jo

Jun 11, 2023

## Dot Product 내적은 두 신호가 얼마나 닮았는냐를 계산해주는 일이기도 함 [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)

0362165a5a3d490784d9c3ff41b2b19f

Outer Product

Vector Operations

Jan 23, 2022

Alan Jo

Apr 6, 2023

## Cross Product - Anti [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a) $$\vec{u} \times \vec{v} = - \vec{v} \times \vec{u}$$

4106750021e944d985d7fdb1b42570ae

Vector Addition

Vector Operations

Jan 23, 2022

Alan Jo

Apr 6, 2023

move origin

e75327dc94934cbb895656ca08112007

Vector Multiplication

Vector Operations

Jan 23, 2022

Alan Jo

Apr 6, 2023

### scaling scalars - change length scaler can be [Commutative Property](https://texonom.com/commutative-property-216366d94b2d43fb87d11e87cc3a233a)

aa46ebeebb3a4aa2bdd459a13dc655dd

Basis Vector

Vector Space Notion

May 23, 2023

Alan Jo

May 23, 2023

374bc63669314745b4513e0ba77704d5

Inner Product space

Vector Space Notion

Jun 6, 2023

Alan Jo

Jun 6, 2023

47e25eabbade4a0f923601f5f58255b2

Subspace

Vector Space Notion

May 23, 2023

Alan Jo

May 23, 2023

e559a723195a4ae5bda391c3332695d6

Vector Equation

Vector Usages

Oct 31, 2022

Alan Jo

Oct 31, 2022

### Vector Equations |Title| |:-:| |[Vector Equation of a Plane](https://texonom.com/vector-equation-of-a-plane-1f3a37a903984921bf16acf5bc138678)| |[Vector Equation of a Line](https://texonom.com/vector-equation-of-a-line-40c9a0f52a944427a5c69456ca4b429c)|

122ad1c33c514ad3b2c9cee4aac00521

Vector Similarity

Vector Usages

Apr 28, 2023

Alan Jo

Jun 5, 2023

[Latent Space](https://texonom.com/latent-space-d67b6bdef18b4058bfbc3d25f87ec087)

## Vectorized Pairwise Similarity $$<a, b>$$ - [Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f) - [Euclidean Distance](https://texonom.com/euclidean-distance-0d3a8b5dc5e04ee595dc85365b2d3fd9) ### Pairwise similarity matrix result value ### Vector Similarities |Title| |:-:| |[Cosine Similarity](https://texonom.com/cosine-similarity-0686a915d71749b6aecbe611fd0f3efd)| ### Vector Similarity Algorithms |Title| |:-:| |[HNSW Algorithm](https://texonom.com/hnsw-algorithm-2d387cef1103477f99d181e956f3d76d)| |[KNN Algorithm](https://texonom.com/knn-algorithm-3b5f079c416349f5af4a54537c873d4b)| |[Annoy Algorithm](https://texonom.com/annoy-algorithm-b91a06fdf7a64255a3f0452b28abd4df)| ### Vector Similarity Tools |Title| |:-:| |[Faiss](https://texonom.com/faiss-445af9045d9c486995f31a2e75cff3ba)|

846675a408e74235acc836302110ab07

Vector Equation of a Line

Vector Equations

Oct 31, 2022

Alan Jo

Oct 31, 2022

$$x = \vec{endpoint} + t \cdot\vec{direction}$$ if (t>0), it is ray if t has a range, it is segment ### distance between one straight line and one point $$D = \frac{\vec{AP} \times \vec{d}} {\vec{d}} = \overline{AP}sin{\theta} $$ ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fa06502d3-f475-42a8-9c24-b65400835101%2FUntitled.png?table=block&id=88cf7bf2-f7b0-418f-a07e-a8181bc2a73d&cache=v2) ### Distance between two lines $$\vec{a_1} + t\cdot\vec{b_1}\vec{a_2} + t\cdot\vec{b_2}d = |\frac{(\vec{a_2} - \vec{a_1}) \cdot (\vec{b_1}\times \vec{b_2}) } {|\vec{b_1} \times \vec{b_2}|}|$$ > [Lesson Explainer: The Perpendicular Distance between Points and Straight Lines in Space | Nagwa](https://www.nagwa.com/en/explainers/939127418581/) > [Shortest Distance Between Two Lines in 3D](https://www.youtube.com/watch?v=6vpXM1dskmY)

40c9a0f52a944427a5c69456ca4b429c

Vector Equation of a Plane

Vector Equations

Oct 31, 2022

Alan Jo

Oct 31, 2022

$$\vec{normal} \cdot(\vec{x} - \vec{point}) = 0$$ > [Lesson Explainer: Equation of a Plane: Vector, Scalar, and General Forms | Nagwa](https://www.nagwa.com/en/explainers/373101390857/)

1f3a37a903984921bf16acf5bc138678

Cosine Similarity

Vector Similarities

Mar 10, 2023

Alan Jo

Jun 1, 2023

차원이 높아질수록 [Curse of dimensionality](https://texonom.com/curse-of-dimensionality-343455a61aa14779b6edf4c93464fac3) 때문에 거리파악은 의미가 적어진다 그래서 유사도 각도로 계산

0686a915d71749b6aecbe611fd0f3efd

Annoy Algorithm

Vector Similarity Algorithms

Jun 1, 2023

Alan Jo

Jun 1, 2023

## Approximate Nearest Neighbors [annoy](https://github.com/spotify/annoy) - 근사해서 가까운 벡터 찾음 - 데이터 추가가 어렵다

b91a06fdf7a64255a3f0452b28abd4df

HNSW Algorithm

Vector Similarity Algorithms

Jun 1, 2023

Alan Jo

Jul 13, 2023

[Small worlds Network](https://texonom.com/small-worlds-network-b779baa02bc846b5970d67d561d755c0)

## Hierarchical Navigable Small words ![https://forward.nhn.com/2022/sessions/42](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2981ffe8-e2f7-403e-9cb5-50718e3bc8c4%2FUntitled.png?table=block&id=612850c1-5f74-400f-864c-92e75bd01de4&cache=v2) ### HNSW Algorithm Notion |Title| |:-:| |[Probability Based Skip List](https://texonom.com/probability-based-skip-list-9111e1422511456bbfb7e7c3fa227860)| ### HNSW Algorithm Tools |Title| |:-:| |[HNSWlib](https://texonom.com/hnswlib-11dcfb3c5e5d448da1b0c7be3998520e)| |[](https://texonom.com/b47fdad5d11f4717974fc3aac3d667bd)| > [대충? 거의 정확하다! 벡터 검색 엔진에 ANN HNSW 알고리즘 도입기 (feat. SWIG Golang)](https://forward.nhn.com/2022/sessions/42)

2d387cef1103477f99d181e956f3d76d

KNN Algorithm

Vector Similarity Algorithms

Jun 1, 2023

Alan Jo

Jun 1, 2023

3b5f079c416349f5af4a54537c873d4b

Probability Based Skip List

HNSW Algorithm Notion

Jun 1, 2023

Alan Jo

Jun 1, 2023

![https://forward.nhn.com/2022/sessions/42](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F9274bee0-ec54-41d1-9bbb-53d66cb16311%2FUntitled.png?table=block&id=7014159d-9f00-4e50-8211-65fc8d4f0d39&cache=v2)

9111e1422511456bbfb7e7c3fa227860

[pg_embedding](https://github.com/neondatabase/pg_embedding)

HNSW Algorithm Tools

Jun 1, 2023

Alan Jo

Jul 13, 2023

b47fdad5d11f4717974fc3aac3d667bd

HNSWlib

HNSW Algorithm Tools

Jun 1, 2023

Alan Jo

Jun 1, 2023

11dcfb3c5e5d448da1b0c7be3998520e

[hnswlib-node](https://github.com/yoshoku/hnswlib-node)

HNSWlib Usages

Jun 1, 2023

Alan Jo

Jun 1, 2023

2ab069bd60b3423faa91c460afa92955

hnswlib python

HNSWlib Usages

Jun 6, 2023

Alan Jo

Jun 6, 2023

[hnswlib](https://github.com/nmslib/hnswlib) ### Index space > [How to use the hnswlib.Index function in hnswlib | Snyk](https://snyk.io/advisor/python/hnswlib/functions/hnswlib.Index)

8b119e7305e74014b4761b8c40404767

Faiss

Vector Similarity Tools

Mar 10, 2023

Alan Jo

Apr 28, 2023

> [Faiss 시작하기](https://velog.io/@nawnoes/Faiss-시작하기)

445af9045d9c486995f31a2e75cff3ba

**BLAS**

Linear Algebra Usages

Feb 21, 2022

Alan Jo

Jun 5, 2023

## Basic Linear Algebra Subprograms [nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c) > [세상을 바꾼 10개의 컴퓨터 코드 - Sciencetimes](https://www.sciencetimes.co.kr/news/%ec%84%b8%ec%83%81%ec%9d%84-%eb%b0%94%ea%be%bc-10%ea%b0%9c%ec%9d%98-%ec%bb%b4%ed%93%a8%ed%84%b0-%ec%bd%94%eb%93%9c/)

17d8d7491b2147829b88426574733651

Vectorious

Linear Algebra Usages

Jun 5, 2023

Alan Jo

Jun 5, 2023

[vectorious](https://github.com/mateogianolio/vectorious) Node js [N-API](https://texonom.com/n-api-8f1b5ef6b76847deb6e7dd2c688b82fd) [nblas](https://texonom.com/nblas-e7eb59d9195848f78ee8e73cd23e916c)

fd5a587523a9423089cf74ae0899b8ce

nblas

BLAS

null

e7eb59d9195848f78ee8e73cd23e916c

Arithmetic Precision

Arithmetic Notion

Dec 17, 2021

Alan Jo

Jun 6, 2023

정밀도 산술 ### Highest-order operand

baffc5389f06430eb20806e985685c9b

Elementary arithmetic

null

57a9f00b3f30433299816f32b4d49fbd

**Fixed-point arithmetic**

Arithmetic Notion

Dec 17, 2021

Alan Jo

Jun 6, 2023

> [Fixed-point arithmetic - Wikipedia](https://en.wikipedia.org/wiki/Fixed-point_arithmetic)

c46e0722c58c4e2fbc1d2f7027bf6fbe

The Tower Function

Calculus Examples

Aug 23, 2020

Alan Jo

Aug 29, 2021

> [밑이 무한히 계속 생기는 함수 2탄 | The Power Tower Function](https://www.youtube.com/watch?v=doItxhmZavo) > [역사상 최고의 수학자도 알 수 없었던 함수 #Shorts](https://www.youtube.com/watch?v=GPe9Lt8OAdM)

7a63cab2617a402782fbf88c9055d43c

Concave Point

Calculus Notion

Mar 9, 2023

Alan Jo

Mar 9, 2023

c3f6835eb9ef4378830d3b916da3f074

Convex Point

Calculus Notion

Mar 9, 2023

Alan Jo

Mar 9, 2023

160b14cc61114a8a9be9797578e11c7a

Derivation

Calculus Notion

Aug 29, 2021

Alan Jo

Jun 11, 2023

[Vector Field](https://texonom.com/vector-field-ff7ea488edb74510a51e844eee7a222f) [Scalar Field](https://texonom.com/scalar-field-a0e05a5b310c4a6283bc214ec02383e0)

## Differentiation ### Derivation Notion |Title| |:-:| |[Differential Equation](https://texonom.com/differential-equation-419a4e3d42924ec79afc700734b88996)| |[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb)| |[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)| |[Divergence](https://texonom.com/divergence-d8b434d51ae549db839bf075fa2452bb)| |[Curl](https://texonom.com/curl-5472397a80234ddeb5d8dca28b9ccae2)| |[Del](https://texonom.com/del-f6d1cdf554914c98a06c1180179bf401)| |[Antiderivative](https://texonom.com/antiderivative-7e0e92c4cdcb4bc48c323100aa512c81)| > [Gradient, Divergence, Curl에 대하여.](https://sillurian.tistory.com/10)

79d0547aee0d45ce93cdae0f26bc3ce6

Explicit Function

Calculus Notion

Nov 14, 2022

Alan Jo

Mar 9, 2023

### 양함수 종속변수와 독립변수들이 분리된 함수

df8104e2876c42e9b112f6308718e3bc

Implicit Function

Calculus Notion

Nov 14, 2022

Alan Jo

Dec 5, 2022

[Normal Vector](https://texonom.com/normal-vector-84412bdb0b8c43e3a206cd54bc9901f7)

### 음함수 종속변수가 독립변수와 분리되지 않은 하나의 관계식 ### Implicit Function Notion |Title| |:-:| |[Implicit Function Theorem](https://texonom.com/implicit-function-theorem-37a2205114464b178be0937046505686)|

1e383ff61a8b4831abca72e4c37649bd

I**nflection point**

Calculus Notion

Jan 11, 2022

Alan Jo

Jan 11, 2022

변곡점

6448287d912942cea85ee85a981505d6

Integral

Calculus Notion

Apr 5, 2022

Alan Jo

Apr 5, 2022

### Integral Notion |Title| |:-:| |[Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)| |[Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)|

ed91b8e9d33d49bfa6a32e93f7bfdfca

Local extremum point

null

f7a7579a29474436b2a8670a28fed921

Vector Calculus

Calculus Notion

Oct 30, 2022

Alan Jo

Oct 30, 2022

[Vector](https://texonom.com/vector-9ed4d1c8519c496dbfadb1f6b3522255)

### Vector Calculus Notion |Title| |:-:| |[Vector Differential Operator](https://texonom.com/vector-differential-operator-4f2b33fb3ea348ba978e3d117c8246a4)| |[Vector Integral Theorem](https://texonom.com/vector-integral-theorem-2295053d5673460a927e2479d83070b8)| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)

77976c6127ad49c9a6611e16a40f337f

Curl

Derivation Notion

Jun 11, 2023

Alan Jo

Jun 11, 2023

[Outer Product](https://texonom.com/outer-product-4106750021e944d985d7fdb1b42570ae)

Derivative which map Vector field to Vector field ### describes the infinitesimal circulation of a vector field ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fd5c23481-3bb4-4f34-ac18-532b99d81275%2FUntitled.png?table=block&id=53692b35-0349-441c-a6e1-a344c3881ca4&cache=v2) ### Curl Notion |Title| |:-:| |[Stokes' theorem](https://texonom.com/stokes-theorem-d3b508adeddc45c98a0f27d792b17999)| > [Curl (mathematics)](https://en.wikipedia.org/wiki/Curl_(mathematics))

5472397a80234ddeb5d8dca28b9ccae2

Del

Derivation Notion

May 6, 2023

Alan Jo

Jun 11, 2023

Del operator nabla symbol $$\nabla$$

f6d1cdf554914c98a06c1180179bf401

Derivative

Derivation Notion

Oct 30, 2022

Alan Jo

May 6, 2023

[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)

### Derivative Notion |Title| |:-:| |[Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)| |[Chain Rule](https://texonom.com/chain-rule-cdc4287f5b2a4bcda97886907836d5d0)| |[Quotient Rule](https://texonom.com/quotient-rule-283d6806817f4684838f842865de0397)|

67f45809e7a84277be4fca74a3b86ceb

Differential Equation

Derivation Notion

Aug 29, 2021

Alan Jo

Jun 15, 2022

419a4e3d42924ec79afc700734b88996

**Divergence**

Derivation Notion

Jun 11, 2023

Alan Jo

Jun 11, 2023

[Inner product](https://texonom.com/inner-product-0362165a5a3d490784d9c3ff41b2b19f)

## Vector field to multi variable scalar function ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5f8b43e7-da4b-427a-accd-e85df5fa9ddc%2FUntitled.png?table=block&id=1f1ae617-32ae-4409-9db9-ada1dc25261d&cache=v2) ### **Divergence Notion** |Title| |:-:| |[Gauss Divergence Theorem](https://texonom.com/gauss-divergence-theorem-6b5f20e56c78488997efddf7f1fd2ebf)| > [Divergence](https://en.wikipedia.org/wiki/Divergence)

d8b434d51ae549db839bf075fa2452bb

Gradient

Derivation Notion

Mar 16, 2023

Alan Jo

Jun 11, 2023

### Derivate multi variable scalar function to vector field using [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9) ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F78130f9f-bc29-4ee5-9b29-6a32246a0d4d%2FUntitled.png?table=block&id=246a18b6-2d4a-4f04-bd4e-a5e6c984fd37&cache=v2) 2차일 때 등고선 개념으로 이해하면 쉽다. 그래디언트의 크기는 경사도 > [Gradient, Divergence, Curl에 대하여.](https://sillurian.tistory.com/10) > [수학 - Divergence ,Gradient, Curl[미완]](https://m.blog.naver.com/ptm0228/221676279348) > [Gradient](https://en.wikipedia.org/wiki/Gradient)

685dfab242a4421da9f5bd89ae5975ed

**Stokes' theorem**

Curl Notion

Jun 11, 2023

Alan Jo

Jun 11, 2023

d3b508adeddc45c98a0f27d792b17999

Chain Rule

null

> [Chain rule](https://en.wikipedia.org/wiki/Chain_rule)

cdc4287f5b2a4bcda97886907836d5d0

Partial Derivative

Derivative Notion

Oct 30, 2022

Alan Jo

May 6, 2023

[Gradient](https://texonom.com/gradient-685dfab242a4421da9f5bd89ae5975ed)

다변수 함수의 특정 변수를 제외한 나머지 변수를 상수로 간주하여 미분하는 것 Nabla와 혼용하지 않기 ### partial f partial x $$\frac{\partial f}{\partial x}$$ $$\lim_{h\rightarrow 0}\frac{f(x +h,y) - f(x,y)} {x + h - x}$$ ### Partial Derivative Notion |Title| |:-:|

e9c7ff432f1c43af8669ef0addd78cd9

Quotient Rule

Derivative Notion

Jun 6, 2023

Alan Jo

Jun 6, 2023

283d6806817f4684838f842865de0397

Laplace Transform

Differential Equation Methods

Jun 15, 2022

Alan Jo

Sep 13, 2023

[Pierre-Simon Laplace](https://texonom.com/pierre-simonlaplace-9a48a934756544579f8398d8a349029b)

ln으로 처리하고 미분방정식 처리에 용이하다 발산하는 함수에 대한 [Fourier Transform](https://texonom.com/fourier-transform-5ee1f9063a9743dd9846ddc600286d5a)을 적용하기 위한 방법 ### Laplace Transform Notion |Title| |:-:| > [7분만에 이해해보는 라플라스 변환](https://www.youtube.com/watch?v=4ONICadjLBY)

155ade7fe1bc4712b183339c25d68fda

****Gauss Divergence Theorem****

Divergence Notion

Jun 11, 2023

Alan Jo

Jun 11, 2023

[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f) [Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)

> [Divergence theorem](https://en.wikipedia.org/wiki/Divergence_theorem) > [Gauss Divergence Theorem. Get the DEEPEST Intuition.](https://www.youtube.com/watch?v=zZqxbwl3Dno)

6b5f20e56c78488997efddf7f1fd2ebf

Implicit Function Theorem

Implicit Function Notion

Nov 14, 2022

Alan Jo

Nov 14, 2022

> [Implicit function theorem - Wikipedia](https://en.wikipedia.org/wiki/Implicit_function_theorem)

37a2205114464b178be0937046505686

Lebesgue integral

Integral Notion

Apr 5, 2022

Alan Jo

Jun 11, 2023

[Measure Theory](https://texonom.com/measure-theory-4fb6210801ea4d7abcb937cd068ba461) [Riemann integral](https://texonom.com/riemann-integral-47f26748e1174265ae26d8a12b04fdca)

### 르베그 적분 일반적인 측도 공간 위에 정의될 수 있는 적분 실수선 위에서의 르베그 적분은 리만 적분보다 더 일반적 리만 적분이 정의되지 않아도 르베그 적분이 정의되는 함수들이 존재 ### Lebesgue integrals |Title| |:-:| |[Surface Integral](https://texonom.com/surface-integral-29bad5fdca49449bb4a96603905b160f)| |[Volume integral](https://texonom.com/volume-integral-41bc72e8ff194d54b11f16135b751348)| > [르베그 적분 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EB%A5%B4%EB%B2%A0%EA%B7%B8_%EC%A0%81%EB%B6%84)

df7652d80314427db614b002c7a74de0

**Riemann integral**

Integral Notion

Apr 5, 2022

Alan Jo

Apr 15, 2023

[Bernhard Riemann](https://texonom.com/bernhard-riemann-166d61214be5439ca5f7ba1090063a3e) [Lebesgue integral](https://texonom.com/lebesgue-integral-df7652d80314427db614b002c7a74de0)

닫힌구간에 정의된 실숫값 함수의 적분의 종류 정의역 구간을 잘게 나눠, 각각의 작은 구간 위의 넓이를 직사각형의 넓이를 통해 근사

47f26748e1174265ae26d8a12b04fdca

Surface Integral

Lebesgue integrals

Jun 11, 2023

Alan Jo

Jun 11, 2023

29bad5fdca49449bb4a96603905b160f

****Volume integral****

Lebesgue integrals

Jun 11, 2023

Alan Jo

Jun 11, 2023

41bc72e8ff194d54b11f16135b751348

Vector Differential Operator

Vector Calculus Notion

Oct 30, 2022

Alan Jo

Oct 30, 2022

[Derivation](https://texonom.com/derivation-79d0547aee0d45ce93cdae0f26bc3ce6)

### Vector Differential Operators |Title| |:-:| |[Vector Curl](https://texonom.com/vector-curl-17571a486321485e80a305ac4bb93e19)| |[Gradient Vector](https://texonom.com/gradient-vector-d3940976683946f89bd512d0bbf45672)| |[Vector Divergence](https://texonom.com/vector-divergence-0ee28e695ecd48a68665f8a30cb7c864)| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)

4f2b33fb3ea348ba978e3d117c8246a4

Vector Integral Theorem

Vector Calculus Notion

Oct 30, 2022

Alan Jo

Oct 30, 2022

### Vector Integral Theorems |Title| |:-:| > [Vector calculus - Wikipedia](https://en.wikipedia.org/wiki/Vector_calculus)

2295053d5673460a927e2479d83070b8

Gradient Vector

Vector Differential Operators

Oct 30, 2022

Alan Jo

Oct 7, 2022

[Derivative](https://texonom.com/derivative-67f45809e7a84277be4fca74a3b86ceb) [Partial Derivative](https://texonom.com/partial-derivative-e9c7ff432f1c43af8669ef0addd78cd9)

$$\vec{z}, \vec{x} \text{ } is \text{ } \text{ on the surface } f(\vec{x}) = 0$$ $$\vec{z} = \vec{x} + \epsilon\vec{u} $$ $$f(z) = f(x + \epsilon u) - f(x_1 + \epsilon u_1, x_2 + \epsilon u_2, x_3 + \epsilon u_3)$$ $$h(x, y, z) = 0$$ $$\nabla h = (\frac{dh}{dx}, \frac{dh}{dy}, \frac{dh}{dz})$$ 심플하게 편미분으로 구해도 되고 $$\nabla h = \frac{d\vec{h}}{dx} \times \frac{d\vec{h}}{dy}$$ xy 아니더라도 곡면의 해당 접평면상에서 움직이는 거라 yz나 xz 도 가능 > [Untitled](https://www.cs.ucr.edu/~craigs/courses/2022-fall-cs-130/lectures/normals.pdf)

d3940976683946f89bd512d0bbf45672

Vector Curl

Vector Differential Operators

Oct 30, 2022

Alan Jo

Oct 30, 2022

**회전 Operator** 3차원 벡터장을 다른 3차원 벡터장으로 대응시키는 1차 미분 연산자의 하나

17571a486321485e80a305ac4bb93e19

Vector Divergence

Vector Differential Operators

Oct 30, 2022

Alan Jo

Oct 30, 2022

0ee28e695ecd48a68665f8a30cb7c864

Butterfly Effect

Chaos Theory Notion

Jun 22, 2021

null

62e1b65850da4b3ab2d429292473f8a1

Complex System

Chaos Theory Notion

May 16, 2022

null

> [Complex system - Wikipedia](https://en.wikipedia.org/wiki/Complex_system)

b2457d8f6fcc4fe2abffd71828908a1f

Lorenz Attractor

Chaos Theory Notion

Jun 22, 2021

null

b3249a819200420797f82e204cc9d58c

Combinatorics

Discrete Math Topics

May 13, 2023

Alan Jo

May 13, 2023

887b47c6bb1c46388a8387d89bd304cf

Order Theory

Discrete Math Topics

May 13, 2023

Alan Jo

May 13, 2023

8c7e8fb9638f41b19b6829d686fc6f9b

**Pigeonhole principle**

Discrete Math Topics

Nov 5, 2019

Alan Jo

Seong-lae Cho

May 13, 2023

비둘기집 원리

998c7a67c04e43d28b132eaa02d5f0d8

Graph Signal Processing

Graph Theory Fields

Apr 28, 2023

Alan Jo

Apr 28, 2023

## GSP > [Untitled](https://web.media.mit.edu/~xdong/talk/BDI_GSP.pdf)

a6551be225984e4cad9bdd244d6a58b5

Dynamical System

Ergodic theory Notion

Apr 3, 2022

Alan Jo

Aug 28, 2023

### Dynamical System Notion |Title| |:-:| |[Dynamical systems theory](https://texonom.com/dynamical-systems-theory-b693764c797945f1b330d386a85ad936)| |[Logistic Map](https://texonom.com/logistic-map-d968681610c749e9983e28f97ee5c50b)| > [Dynamical system - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_system)

a4e33185067b49b28e8f62454028f7b1

Poincare R**ecurrence **Theorem

Ergodic theory Notion

Nov 13, 2019

Alan Jo

Jul 12, 2023

[Grigori Perelman](https://texonom.com/grigori-perelman-c53487e421c94fceb6a83431c7cc1149) [Henri Poincare](https://texonom.com/henri-poincare-1382da083d864065972f27c140c4aa64)

### 푸앵카레 재귀 정리 특정한 계는 충분한 시간이 지난 후에는 초기상태와 아주 가까운 상태로 회귀한다는 내용의 정리 에너지 준위가 이산적인 양자역학적 계에 대해서도 비슷한 정리가 성립 > [Poincaré recurrence theorem - Wikipedia](https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem)

1aca4c4a3d2446c1892de56b1071953c

**Dynamical systems theory**

Dynamical System Notion

Apr 3, 2022

Alan Jo

Apr 3, 2022

> [Dynamical systems theory - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_systems_theory)

b693764c797945f1b330d386a85ad936

Category Theory

null

집합론의 반대에 해당하는 개념 요소 대신 요소들 간의 관계에 주목하여 추상적인 개념들을 다루고자 하는 수학 이론 ### Category Theory Notion |Title| |:-:| |[Topos Theroy](https://texonom.com/topos-theroy-cd8c3fed6bb14e8cbda9294ed472a4df)| > [Category theory](https://en.wikipedia.org/wiki/Category_theory)

1b6594b7d4ce4c128ec2f9aed95d9f3c

Gödel’s incompleteness theorem

Foundations of Mathematics Notion

May 30, 2021

Alan Jo

Sep 17, 2023

1차 논리에서 증명 가능한 명제의 집합은 모형을 갖는다는 정리 수리논리학 즉, 증명 이론으로 정의한 진리와 모형 이론으로 정의한 진리가 서로 일치 을 피하기 위해 아무리 세심하게 공리계를 설계해도 그것을 피할 수는 없다는 것을 증명하였으며, 이것이 불완전성 정리 [2nd Gödel’s incompleteness theorem](https://texonom.com/2nd-gdels-incompleteness-theorem-173d1bd5bdac42448e637253f602a763) > [Zarathu Blog: 괴델의 불완전성 정리](https://blog.zarathu.com/posts/2019-05-20-godelincompleteness/) > [괴델의 불완전성 정리](https://jinseob2kim.github.io/godel.html) > [괴델의 완전성 정리 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EA%B4%B4%EB%8D%B8%EC%9D%98_%EC%99%84%EC%A0%84%EC%84%B1_%EC%A0%95%EB%A6%AC) > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw)

820d082fd9bf424f8125dda3bf9e859b

**Langlands program**

Foundations of Mathematics Notion

Aug 25, 2022

Alan Jo

Aug 25, 2022

[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2) [Harmonic Analysis](https://texonom.com/harmonic-analysis-e1e54ebeffd0407088bebab57acbfd53)

대수적 수 이론에서 갈루아 군들을 보형 형식에 관련시키고 국소체와 아델 환에 대한 대수적 그룹의 표현 이론을 서로 연관짓는 광범위한 영향력 있는 추측의 망 로버트 랭글랜즈에 의해 제안 > [The Biggest Project in Modern Mathematics](https://youtu.be/_bJeKUosqoY)

629d720ec59b4bf4a42c0b066675b220

Set Theory

null

### Set Theory Notion |Title| |:-:| |[Russell's paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)| |[Infinite Set](https://texonom.com/infinite-set-971d3736190a4752a1ee3d1e2fea7028)| |[Cantor's theorem](https://texonom.com/cantors-theorem-3057f62f2b4947448aaf1c7a0fd8904d)| |[Power Set](https://texonom.com/power-set-58038c26c9ef49e1bf59cae859c90394)| |[Continuum Hypothesis](https://texonom.com/continuum-hypothesis-8792f326812a41d0b546db08fbd82a52)| |[Diagonal Argument](https://texonom.com/diagonal-argument-8a8921d2ba3745a199517d8650d50395)| |[Countable Set](https://texonom.com/countable-set-94c63f44bb5c4334857afe94d13cad59)| |[Uncountable Set](https://texonom.com/uncountable-set-287e751cba3c466e92f123ca2f04e13f)| |[Infinite Set](https://texonom.com/infinite-set-93755bd42acf41e2ac688467ad687885)| |[Finite Set](https://texonom.com/finite-set-63ed2bdb689946429effb738e5422255)| |[Cantor’s paradox](https://texonom.com/cantors-paradox-c84022d0e5e344889da73daf136602ce)| |[Naive set theory](https://texonom.com/naive-set-theory-67e68d75439f41bb8eb032834706044d)| |[Equinumerosity](https://texonom.com/equinumerosity-907dd17f4fab4b9b8212011bc680e5bf)| |[Cantor set](https://texonom.com/cantor-set-9cfdfcff7f82497eaca09074d723a722)| |[Complement Set](https://texonom.com/complement-set-2ed91c78263a44a18c5a65ab86be77db)| |[Symmetric difference](https://texonom.com/symmetric-difference-07bdea8546c04dabb5cd4ec7fd61b67b)| |[Poset](https://texonom.com/poset-9a126737d3414bfc9225fe391603b9ad)| |[Borel set](https://texonom.com/borel-set-76ba23edebd64061af05154588ab2870)| |[ZFC](https://texonom.com/zfc-f844451d3f134288a92febc7b8e8257b)| > [Untitled](https://www.math.snu.ac.kr/~kye/lecture/02_1_set_theory/%BE%E7%C0%BA%C7%FD.htm) ### Set > [MySQL 합집합, 교집합, 차집합, 대칭차](https://zetawiki.com/wiki/MySQL_%ED%95%A9%EC%A7%91%ED%95%A9,_%EA%B5%90%EC%A7%91%ED%95%A9,_%EC%B0%A8%EC%A7%91%ED%95%A9,_%EB%8C%80%EC%B9%AD%EC%B0%A8)

a74b3919af5e4e6e885862f6f76103f9

Type Theory

Foundations of Mathematics Notion

May 13, 2023

Alan Jo

May 13, 2023

a6967220456b47498b951f11598381f7

Topos Theroy

Category Theory Notion

Jul 12, 2023

Alan Jo

Jul 12, 2023

### Topos Theroy Notion |Title| |:-:| |[Topos](https://texonom.com/topos-6d05bbca3e3d4051bc512027cb7543ef)| |[Elementary Topoi](https://texonom.com/elementary-topoi-99bdc34b5e4a47e3b3597391ceb5ea7a)| |[Grothendieck tp[po](https://texonom.com/grothendieck-tppo-76ca3dfbb8b644648d81fd583eefbf28)| > [Topos](https://en.wikipedia.org/wiki/Topos)

cd8c3fed6bb14e8cbda9294ed472a4df

E**lementary Topoi**

Topos Theroy Notion

Jul 12, 2023

Alan Jo

Jul 12, 2023

[Logic](https://texonom.com/logic-e562053ace984677a72cb9eaf5c6f91e)

99bdc34b5e4a47e3b3597391ceb5ea7a

Grothendieck tp[po

Topos Theroy Notion

Jul 12, 2023

Alan Jo

Jul 12, 2023

[Algebraic Geometry](https://texonom.com/algebraic-geometry-4dc98f1cbfff43e1b969e0b660c484c2)

76ca3dfbb8b644648d81fd583eefbf28

Topos

Topos Theroy Notion

Jul 12, 2023

Alan Jo

Jul 12, 2023

[Sheaf](https://texonom.com/sheaf-c1aa0624425d40ab86351c509a86b389)

### 일반화된 공간 개념들을 일반화시켜서 다루는 것

6d05bbca3e3d4051bc512027cb7543ef

2nd Gödel’s incompleteness theorem

Gödel’s incompleteness theorem

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> [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw)

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**Borel set**

Set Theory Notion

Mar 27, 2023

Alan Jo

Mar 27, 2023

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**Cantor set**

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 15, 2023

### 비가산 무한집합 실수에서 닫힌 구간 \left[0, 1 \right] [0,1]를 3등분해나가면서 가운데 것을 제거하는 작업을 반복하여 얻는 집합 비가산 집합임에도 측도가 0인 집합 즉 길이가 0이다 프랙털의 일종 0과 1사이의 실루로 이루어진 집합이고 3등분해서 가운데 구간을 반복적으로 제외하는 방식으로 만든다 조밀한 곳이 없는 완전집합 [Cantor function](https://texonom.com/cantor-function-bab4b944c0cb44bdb0089d40ec6b1542) > [Cantor set - Wikipedia](https://en.wikipedia.org/wiki/Cantor_set)

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Cantor’s paradox

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 5, 2022

[Russell's paradox](https://texonom.com/russellsparadox-7ecbb574edd24c5ab9066b8a5fcc6dea)

모든 집합들의 모임이 집합을 이룰 수 없다

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Cantor's theorem

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 5, 2022

멱집합의 크기가 항상 원래의 집합의 크기보다 크다는 정리 즉 집합과 멱집합의 원소는 일대일 대응할 수 없다 > [칸토어의 정리 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EC%B9%B8%ED%86%A0%EC%96%B4%EC%9D%98_%EC%A0%95%EB%A6%AC)

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Complement Set

Set Theory Notion

Oct 31, 2022

Alan Jo

Oct 31, 2022

2ed91c78263a44a18c5a65ab86be77db

Continuum Hypothesis

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 5, 2022

**연속체 가설** 표준적 공리계로는 증명할 수도, 반증할 수도 없다 실수 집합의 모든 부분 집합은 가산집합이거나 아니면 실수 집합과 크기가 같다는 명제 힐베르트 문제의 1번

8792f326812a41d0b546db08fbd82a52

Countable Set

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 15, 2023

### 가산집합 자연수 정수는 가산이고 유리수도 가산인데 실수는 비가산

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Diagonal Argument

Set Theory Notion

Apr 5, 2022

Alan Jo

Apr 5, 2022

칸토어가 실수가 자연수보다 많음을 증명하는 데 사용한 방법 실수 집합이 비가산집합임을 보이는 데 사용된다 > [대각선 논법 - 위키백과, 우리 모두의 백과사전](https://ko.wikipedia.org/wiki/%EB%8C%80%EA%B0%81%EC%84%A0_%EB%85%BC%EB%B2%95)

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