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Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
with the rest of them being set on a secondary position. Chemical manufacturer website β UX Design Dedicated Sustainability Section The majority of chemical manufacturing websites contain a section dedicated to sustainability. This is mainly because of possible scrutiny concerning their impact on | medium | 3,977 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
the environment. A dedicated section that addresses these points can point towards a more transparent image which in turn leads to trust. This also contributes to their overall image as a member of the industry. Companies can showcase their positive actions, increasing their reputation and their | medium | 3,978 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
business intake. Demonstrating dedication to sustainability and environmental causes can also be a ramp towards more popularity and thus, a step up from the competitors. Discover professional UX design. Most of the websites use a simple section made out of an image alongside text with a link to a | medium | 3,979 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
dedicated, separate page which can also present a sustainability report. Sabic Sustainability Section While this might be a positive method of doing this, it is not also creative. Wanhua Sustainability Section The example found on Air Liquideβs website is well-done because as the user scrolls | medium | 3,980 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
through this section, the title scrolls horizontally as well. Chemical manufacturer website β UX Design The idea of sustainability is repeated throughout the home page. It would have probably been better if they included more concrete insights which would better show the actions they take towards | medium | 3,981 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
sustainability. This could be done by adding a statistics script in one of the sections. Chemical manufacturer website β UX Design The sustainability element is repeated towards many of the homepages in different ways. In the case of the BASF website, this comes in the form of a case study. | medium | 3,982 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Generally, when an idea is repeated in different ways throughout the website, the user might remember it better. Chemical manufacturer website β UX Design Choosing high-quality images is a great choice for their sustainability section. There is, however, one problem here. Because of the large | medium | 3,983 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
amount of space taken up by the centred paragraph, which occupies much of the gridβs width, the section is hardly readable. Chemical manufacturer website β UX Design Noah Chemicals uses a fitting visual for this section, providing a relevant link to their case study on sustainability. Chemical | medium | 3,984 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
manufacturer website β UX Design Using such a vibrant colour is a good choice, as it draws attention. The problem here is that it fails the contrast test. Chemical manufacturer website β UX Design A good implementation of the sustainability section is the one encountered on the LG Chem website. | medium | 3,985 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Generally, itβs much more impactful to present your results rather than an empty statement where you promise to be sustainable. Chemical manufacturer website β UX Design Links to press releases/news/case studies The press release/news/case studies section is commonly found on homepages, | medium | 3,986 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
irrespective of the industry. This section is a suitable place for regular updates of the companyβs activity. More than this, providing such up-to-date content can improve in terms of SEO, helping the website get more viewers. Clients might also be interested in learning more about the companyβs | medium | 3,987 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
activities, so it serves them too. As a rule of thumb, if a company shares things like insights, research findings and achievements, its status as an expert in the industry is more feasible. Most of the time, news is positioned towards the end of the homepage, incorporated as components with images | medium | 3,988 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
and text. The reason behind this position is based on the importance of each section. Sections such as βNewsβ are at the end of the list for most websites. However this does not mean that such sections are irrelevant, they are essential for companies. The flow of the page usually leads to having | medium | 3,989 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
βnewsβ at the end, as users are met with this section only after having engaged with the other parts of the page. There are not many ways these companies have gone about tackling this type of section. Some examples have been chosen for their creativity and uniqueness. LG Chem brought about a few | medium | 3,990 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
quick filter options which allow users to select the news category they wish to see. The solution used here is quite efficient, especially in such cases where there are multiple types of content. Chemical manufacturer website β UX Design ExxonMobil used a sidebar that contains a text-only list as | medium | 3,991 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
their news section. This solution is beneficial when the aim is to show more content. This news section is positioned towards the top of the page which means it is an important element for them. Chemical manufacturer website β UX Design Dupont chose a more creative layout for their news section, | medium | 3,992 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
highlighting one entry (which is more important for them) and presenting the others in a smaller side panel. This is a good choice because there is a clear hierarchy given to the news, allowing users to easily distinguish which article is more relevant. In the case of Dupont, their most βimportantβ | medium | 3,993 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
piece of news is in regards to their sustainability report β they want to make it more visible to possible clients. The text-only news is, naturally, the most unimportant but despite this, they still provide content variety β this is a plus. Chemical manufacturer website β UX Design Investor | medium | 3,994 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Section This section is present on the majority of chemical manufacturing websites. It is relevant for the following reasons: It offers a place for communication with current and potential investors through annual reports, stock information, governance updates and others. It is sometimes a must for | medium | 3,995 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
public companies to be transparent with their finances. This place is the perfect section to display such information. Most of the time this section can be found either underneath the hero section or towards the end of the page. A common piece of information displayed by these chemical | medium | 3,996 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
manufacturers is their stock price. Chemical manufacturer website β UX Design Chemical manufacturer website β UX Design Evonik does this differently. On their website, they display financial news alongside the share price in this manner. Chemical manufacturer website β UX Design Wanhua has grouped | medium | 3,997 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
stock information with links to their hiring page. This composition does not make much sense and could actually be confusing for those visiting the website. Chemical manufacturer website β UX Design Covestro has a good example of this section on their website. They used the correct layout, with a | medium | 3,998 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
share button on the right and info related to the financial activity on the left. The square found on the right side displays the share price and also plays a visual role as it can attract attention towards this section. Chemical manufacturer website β UX Design Callout Section The callout | medium | 3,999 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
component can be used to draw attention towards a piece of information. These are also very efficient in converting users and can be used as directional cues, guiding users through many areas of interest (from the site). The brand message can also be reinforced with the help of the callout section. | medium | 4,000 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Generally, itβs advisable not to overuse the callout (especially on the same page) as too many of these sections can lead to diminished results. Dupont efficiently incorporates callouts on their homepage. The first section of this type aims to showcase a product, linking towards a separate page | medium | 4,001 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
where more information about the specific product is displayed. Chemical manufacturer website β UX Design The ending of the page contains a section made to guide users in case they get lost on the website β which can be an efficient strategy for maintaining engagement on the website. Chemical | medium | 4,002 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
manufacturer website β UX Design Toray uses the callout section to highlight an article they want to further promote. Chemical manufacturer website β UX Design Another callout variant comes from Chemours, who did not use very saturated colours for their callout. This could be a good strategy, | medium | 4,003 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
especially when a break in the layout is desired. This makes the website less predictable while not drawing all of the attention towards a single piece of information. Chemical manufacturer website β UX Design Trust Proof Section Testimonials are usually good ways of growing the trust instilled by | medium | 4,004 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
a company. It is not a commonly found section on chemical manufacturing websites because many of the companies focus on B2B and as a result, using testimonials does not make much sense. Despite this, there are other ways of ensuring credibility when it comes to sections on the website. Presentation | medium | 4,005 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
sections with companies that have been clients are quite beneficial in demonstrating trust. Pairing these with case studies that go into detail about collaboration works wonders. Dupont has a dedicated section where they showcase collaborations. This consolidates their image as being a vetted, | medium | 4,006 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
trustworthy company. Some visitors might even be swayed by the collaborating companies. This trust can transfer to the main company that presents itself on the website. Chemical manufacturer website β UX Design In short, placing the logos of companies you have collaborated with helps in these ways: | medium | 4,007 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
It consolidates the professional image of the company It proves trustworthiness in business It showcases evidence-based expertise. The same benefits apply to displaying certifications. Chemical manufacturer website β UX Design Parchem has included a testimonials section on their website, helping | medium | 4,008 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
them solidify their activities through social proof and proven experience. This also contributes to the overall diversity of content on their homepage. Chemical manufacturer website β UX Design Careers Section Including a careers section on the homepage is quite logical, as users seeking a job are | medium | 4,009 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
more easily redirected to the appropriate page. This applies to companies where there is a need for a large number of employees. It is not an essential section for a page and should be implemented only if there is an actual need for it. In terms of methods used to incorporate these sections within | medium | 4,010 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
the homepage, there are a few ways seen on the chemical manufacturer websites. Having an image with a link towards the careers page is one method which allows for better highlighting of this section. The amount of space used for this also counts. Chemours uses a careers section that takes up a | medium | 4,011 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
considerable amount of space. Chemical manufacturer website β UX Design Chemical manufacturer website β UX Design Another way of representing this section is through a link. These variants are quite useful as they sort of resemble a form of navigation, yet more visually interesting. Chemical | medium | 4,012 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
manufacturer website β UX Design Chemical manufacturer website β UX Design Chemical manufacturer website β UX Design If more attention to the careers section is desired, the methods seen above are perfect. The section found on the Covestro website is more developed and alongside the button that | medium | 4,013 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
directs users to the careers page, tabs are also available where various content can be seen. The intent of the section is appropriate but it lacks in execution β the lack of an image or a visual makes the section completely uninteresting. Chemical manufacturer website β UX Design Letter from the | medium | 4,014 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
CEO Section This is not necessarily a common section but it appeared on the websites weβve benchmarked. Usually, the homepage should be used to display the company message and to guide users with their actions. The letter from the CEO section could, as a result, occupy too much space which could be | medium | 4,015 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
used for conversion opportunities. It is worth noting that users usually reach such websites with certain objectives in mind β like for example, to learn about the products and services offered by the company, their contact information etc. For what it is worth, the CEO letter is not very relevant | medium | 4,016 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
to such objectives. Despite this, it should not be considered useless, as the idea can sometimes be beneficial to the homepage. If done as a short and engaging section (a video of the CEO instead of an image for example), it could be a quite useful tool in showing the human side of the brand. | medium | 4,017 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Chemours does this right. They have gathered this content into a small section which does not attract too much attention. Chemical manufacturer website β UX Design On the flip side, Sumitomoβs section is not done right. Their version takes up a lot of space and contains a lot of text (in which too | medium | 4,018 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
many topics are combined even if there is a lack of sense). Less text would have sufficed and a video replacing the image would have been just perfect. Chemical manufacturer website β UX Design Asahi Kasei employs a good method of implementing the CEO letter section. They do this by providing a | medium | 4,019 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
link towards a separate page where this message can be found. The problem here stands in their choice of making the image bigger than all of the titles β this is not right as it should not distract the user so much when scrolling through the website. Chemical manufacturer website β UX Design Key | medium | 4,020 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
Takeaways The messages displayed on your homepage should be clearly articulated to accurately display what your company does, its unique proposition and core competencies in chemical manufacturing. The UI should be clean and minimal when it comes to its style. Interactions ought to be thought out | medium | 4,021 |
Chemicals, Chemical Industry, Web Design, UX Design, User Experience.
well and accurate on all resolutions. Repeated signs of trust will establish credibility in the industry. This is something that should be common amongst such websites. Check out some more of our recent research & benchmarking articles: Law Firm Websites Best Design Practices HR Software Design | medium | 4,022 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
A new epoch in our intellectual evolution. GPT Summary: represents a new era in our intellectual evolution, symbolizing the fusion of human collective knowledge with our expanding artificial intelligence capabilities, primarily through Large Language Models (LLMs) like GPT. LLMs act as a vibrant | medium | 4,024 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
intersection between human and digital realms, processing, predicting, and generating human-like text based on an extensive repository of data. The emergence of such models prompts us to reevaluate our understanding of knowledge, intelligence, and consciousness, highlighting the symbiosis between | medium | 4,025 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
human and artificial cognition. The interaction with these LLMs allows us to engage with and expand our collective knowledge, leading to new intellectual narratives and philosophical debates. This marks a significant step into unexplored intellectual territory, wherein weβre not only creators but | medium | 4,026 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
active participants in this cognitive journey. Our journey as a civilization is a testament to our relentless pursuit of understanding the complex tapestry of our existence. Our endeavors have led us to establish libraries, devise theories, explore the cosmos, and, most notably, create cutting-edge | medium | 4,027 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
technology. At the forefront of this intellectual odyssey, we find ourselves at the inception of a groundbreaking fusion of our human knowledge and our evolving techno-intelligence: Large Language Models, like GPT, embodiments of the βcorpus cognitionis humanaeβ, the body of human knowledge. A | medium | 4,028 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
Collective Cognitive Repository The manifestation of knowledge within models such as GPT is a grand synthesis of our technological acumen and intellectual faculties. Even though GPT does not possess consciousness, it functions as a vibrant intersection of the human and digital realms, a reflection | medium | 4,029 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
of the intricate cognitive architectures of our time. Constructed to process, predict, and generate human-like text, GPT is more than just a replica of human cognition; it is an extension and expansion of our cognitive capacity. Effectively, it forms a meta-cognitive network, a multi-dimensional | medium | 4,030 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
and dynamic knowledge matrix that evolves from the corpus of human knowledge. From historical data, scientific explorations, cultural narratives, and the continuously unfolding digital dialogues, GPT unifies these disparate streams of information, marking a significant leap in the realm of | medium | 4,031 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
artificial intelligence. Redefining Cognition The emergence of GPT and its counterparts brings with it profound philosophical implications. It nudges us to reconsider our definitions of knowledge, intelligence, and consciousness. The βcorpus cognitionis humanaeβ embodied in these models offers a | medium | 4,032 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
fresh perspective on cognition, one that transcends the boundaries of individual thought processes and the very kinetics of thought processes. The intellectual domain, traditionally reserved for human cognition, is witnessing an intriguing intervention with GPTβs capabilities. This AI modelβs | medium | 4,033 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
impressive ability to interpret, generate, and investigate text based on an extensive repository of data, pushes the boundaries of the cognitive realm. This expansion fuels new debates about the essence of consciousness, the dichotomy between biological and artificial intelligence, and the | medium | 4,034 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
potential for a unique symbiotic relationship between the two. At this crossroads, we find a fascinating convergence of philosophical and scientific thought. Both are making strides in deciphering the intricate enigma of cognition, intelligence, and existence. As these AI models evolve, our | medium | 4,035 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
philosophical frontiers also expand, transforming the exploration of LLMs into a profound intellectual quest. The Corpus as a Catalyst Fundamentally, the evolution of GPT and similar LLMs marks a significant stride into unexplored intellectual territory. This innovative βhumano-technoβ symbiosis | medium | 4,036 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
does not substitute human cognition; instead, it enhances and amplifies it. Through this new cognitive prism, we donβt merely view our collective knowledge but actively engage with it, interact with its intricate networks, and generate new intellectual narratives. The GPT frameworkβs scientific and | medium | 4,037 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
philosophical underpinnings push us to reassess long-standing debates about knowledge and even consciousness. However, this exploration is not unilateral. It represents a dynamic conversation between humans and technology, signifying our collective intellectual voyage into this unchartered | medium | 4,038 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
territory. As we step forward in this fascinating cognitive expedition, itβs crucial to remember that our aim is not just the creation of intelligent machines. Itβs about understanding the depth and breadth of our intelligence and knowledge, about gaining a profound insight into our existence in an | medium | 4,039 |
Artificial Intelligence, Cognition, Knowledge, Philosophy, Gpt 3.
increasingly interconnected and intellectually vibrant world. As we navigate this new epoch of AI, we are more than mere spectators; we are active participants shaping and being shaped by the evolving dynamics of the βcorpus cognitionis humana.β | medium | 4,040 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
Photo by Antoine Dautry on Unsplash In this final article of the three-part series, we will talk about two types of decomposition, specifically LU and Eigen Decomposition. If you haven't read the first two articles, they are linked below: Linear Algebra with NumPy- Part I Linear Algebra with NumPy- | medium | 4,041 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
Part II For this final article, we will combine NumPy and SciPy to perform some decompositions. Part I: Introduction Before jumping into the two decompositions, let's talk a little bit about what matrix decompositions are and why they are helpful. A matrix decomposition or matrix factorization is | medium | 4,042 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
essentially reducing your matrix to a product of matrices. The decomposition is done because it makes performing computations easier on the resulting matrices than on the original matrix. A common analogy for matrix decomposition is the factoring of numbers, such as the factoring of 10 into 2 x 5. | medium | 4,043 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
For this reason, matrix decomposition is also called matrix factorization. Like factoring real values, there are many ways to decompose a matrix, hence there is a range of different matrix decomposition techniques, each helping solve a particular class of problems. Some examples include LU | medium | 4,044 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
decomposition, Eigen decomposition, QR decomposition, & Singular Value decomposition. 1 Part II: LU Decomposition The first type of decomposition we will look at is the LU decomposition. Here the βLβ stands for Lower Triangular Matrix and βUβ stands for Upper Triangular Matrix. This means we | medium | 4,045 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
decompose our original matrix into the product of a lower and upper triangular matrix. This type of decomposition is particularly useful when solving a linear system of equations; because it is much easier to deal with triangular matrices, it is very desirable to decompose matrices into products of | medium | 4,046 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
triangular matrices when solving linear equations. We can write this as: where π΄A is a matrix, πΏL is the lower triangular matrix and πU is the upper triangular matrix. In this article, we will talk about three different ways to decompose a matrix into a lower and upper triangular matrix, and they | medium | 4,047 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
differ in the way they set up the Lower or Upper triangular matrix: Doolittle (ππππ(πΏ)=1) Crout (ππππ(π)=1) Cholesky (ππππ(π)=ππππ(πΏ)) We will dive into each one and show how different setups give us the same result. Doolittle In this method of LU decomposition, the Lower Matrix is set up as: where | medium | 4,048 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
x is any number. Let A be a 3x3 matrix We can set the πΏ and π matrix as: We can calculate the product LU as: We can confirm, that multiplying these two matrices would give us the original matrix A. import numpy as np l = np.array([[1,0,0],[3,1,0],[2,1,1]]) u = np.array([[1,2,4], [0,2,2],[0,0,3]]) | medium | 4,049 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
np.matmul(l,u) Out[3]: array([[ 1, 2, 4], [ 3, 8, 14], [ 2, 6, 13]]) As you can see, the product produces the same matrix A. 2. Crout The second method is Crout. In this method, the upper triangular matrix has 1βs on its diagonal. Taking the same matrix A as an example: We can set the πΏ and π | medium | 4,050 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
matrix as: We can confirm the product of these two matrices would give us the original matrix A. l = np.array([[1,0,0],[3,2,0],[2,2,3]]) u = np.array([[1,2,4], [0,1,1],[0,0,1]]) np.matmul(l,u) Out[5]: array([[ 1, 2, 4], [ 3, 8, 14], [ 2, 6, 13]]) 3. Cholesky Finally, the last method is the Cholesky | medium | 4,051 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
method where both the diagonals of the upper and lower triangular matrix are the same. We will follow the same example as above and decompose the matrix π΄A into the two matrices. In this case We can confirm the product of these two matrices would give us the original matrix A. l = | medium | 4,052 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
np.array([[1,0,0],[3,np.sqrt(2),0],[2,2/np.sqrt(2),np.sqrt(3)]]) u = np.array([[1,2,4], [0,np.sqrt(2),2/np.sqrt(2)],[0,0,np.sqrt(3)]]) np.matmul(l,u) Out[7]: array([[ 1., 2., 4.], [ 3., 8., 14.], [ 2., 6., 13.]]) Now instead of calculating the L and U matrices by hand, the scipy package provides | medium | 4,053 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
the linalg.lu function that gives you the LU decomposition of a matrix. Note that this function uses a slightly different method to calculate the LU Decomposition. The linalg.lu function uses what is called a PLU decomposition. More information about the scipy function can be found here. And more | medium | 4,054 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
information about how the PLU decomposition works can be found here. import scipy import scipy.linalg a = np.array([[1,2,4],[3,8,14],[2,6,13]]) p,l,u = scipy.linalg.lu(a) print("Lower Matrix") print(l) print("\n") print("Upper Matrix") print(u) Lower Matrix [[ 1. 0. 0. ] [ 0.66666667 1. 0. ] [ | medium | 4,055 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
0.33333333 -1. 1. ]] Upper Matrix [[ 3. 8. 14. ] [ 0. 0.66666667 3.66666667] [ 0. 0. 3. ]] The reason why the LU Decomposition is so important is that it gives us an alternative approach to solving linear systems. We know that Gaussian Elimination can be used to solve a linear system of the form | medium | 4,056 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
π΄π₯=π (more information on Gaussian elimination in my first article). However, the algorithm for using Gaussian Elimination takes π(1/3*π^3) operations. This is where LU Decomposition can help. Let's say we have the linear system π΄π₯=π, where the matrix π΄ can be decomposed into a lower and upper | medium | 4,057 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
triangular matrix. What we get is: πΏππ₯=π Let π¦=ππ₯ We can solve the equation πΏπ¦=π using forward substitution in π(π^2) operations. And then we can solve ππ₯=π¦ using back substitution in another π(π^2) step. This reduces the time complexity to π(2*π^2) steps. For large systems, this can reduce the | medium | 4,058 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
time significantly. 2,3 Part III: Eigen Decomposition The next decomposition is the Eigen Decomposition. To find the eigenvector and eigenvalue of a matrix A, we know there exists a non-zero vector π’βC^n for which a scalar π satisfies the following equations: π΄π’=ππ’ We can put the eigenvectors of | medium | 4,059 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
matrix A into a matrix denoted by U, where each column represents an eigenvector of matrix A. The eigenvalues are stored as a diagonal matrix denoted by Ξ. We can rewrite the above equation as: π΄π=Ξπ Solving for A, we get the equation: π΄=πΞπβ1 This gives us the eigendecomposition of matrix A. | medium | 4,060 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
**Note not all matrices have eigenvalues Let's solve an example to see how it works: We have a matrix A From my previous article, we know we can get the eigenvalues and eigenvectors of a 2x2 matrix by solving the characteristic equation πππ‘(π΄βππΌ)=0 which, for a 2x2 matrix is equal to: | medium | 4,061 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
π^2βπππ(π΄)+πππ‘(π΄)=0 Solving the above equation, we get the following eigenvalues: π=β1 & π=β2 The eigenvectors for these corresponding eigenvalues are: For π=β1 For π=β2 We can confirm that the product of these matrices would give us our original matrix A from numpy.linalg import norm U = | medium | 4,062 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
np.array([[1,2],[1,3]]) lam = np.array([[-1,0],[0,-2]]) U array([[1, 2], [1, 3]]) from numpy.linalg import inv A = U @ lam @ inv(U) A array([[ 1., -2.], [ 3., -4.]]) As you can see, this gives us the original matrix A back. We can use the eig function from NumPy to find the eigenvalues and | medium | 4,063 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
eigenvectors along with inv function to confirm as well from numpy import linalg as lg Eigenvalues, Eigenvectors = lg.eig(np.array([ [1, -2], [3, -4] ])) Lambda = np.diag(Eigenvalues) Eigenvectors @ Lambda @ lg.inv(Eigenvectors) Out[12]: array([[ 1., -2.], [ 3., -4.]]) Eigendecompostion plays an | medium | 4,064 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
important role in many machine learning applications. Some machine learning applications include Principal Component Analysis, Spectral Clustering, Computer Vision, and many more.4 References 1 https://machinelearningmastery.com/introduction-to-matrix-decompositions-for-machine-learning/ 2 | medium | 4,065 |
Linear Algebra, Python, Numpy, Matrix Decomposition, Eigenvectors.
https://johnfoster.pge.utexas.edu/numerical-methods-book/LinearAlgebra_LU.html 3 https://www.sciencedirect.com/topics/computer-science/gaussian-elimination 4 https://towardsdatascience.com/the-essence-of-eigenvalues-and-eigenvectors-in-machine-learning-f28c4727f56f | medium | 4,066 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
Table of Contents Understanding ISA-95 Standards ISA-95 Hierarchy (Automation Pyramid) Categories of Information Model Equipment Object Model Information Exchange between Level 4 (ERP) and Level 3 (MES) Manufacturing Operations Management Activity Model Conclusion In todayβs rapidly evolving | medium | 4,067 |
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industrial landscape, data has become a critical asset for organizations seeking to streamline processes, improve efficiency, and gain competitive advantage. The realm of automation, particularly in the context of ISA-95, presents both opportunities and challenges in effectively managing data. This | medium | 4,068 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
blog series examines the challenges of data organization in ISA-95 and explores the concept of a unified namespace and its benefits. We will also outline its implementation, including the use of the ISA-95 Equipment Model Standard and clustering for multi-site data replication. The first blog | medium | 4,069 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
explores the fundamental concepts of the ISA-95 standards, their importance in improving manufacturing processes, and their role in fostering cross-functional collaboration, all of which contribute to the optimization and implementation of traditional industrial operations. Understanding ISA-95 | medium | 4,070 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
Standards The ISA-95 standard, also known as ANSI/ISA-95 or ISA-95, is an international standard developed by the International Society of Automation (ISA). It focuses on the integration of enterprise and control systems within the manufacturing industry. ISA-95 stands for βEnterprise-Control | medium | 4,071 |
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System Integration,β and it provides a framework for designing and implementing interoperability between an organizationβs business and manufacturing processes, with the goal of improving the interactions between them. The primary goal of ISA-95 is to establish a common language and structure for | medium | 4,072 |
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communication and data exchange between different levels of an organization, ranging from the enterprise level, where business decisions are made, down to the control level, where real-time production processes are managed. This standard helps bridge the gap between the information technology (IT) | medium | 4,073 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
and operational technology (OT) domains. ISA-95 Hierarchy (Automation Pyramid) The Manufacturing Automation Pyramid is a conceptual representation of ISA-95 hierarchy that is often associated with industrial automation and control systems. The Automation Pyramid, also known as the automation | medium | 4,074 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
hierarchy of βIndustrial 3.0β, illustrates the hierarchical structure of control and automation systems within industrial environments. Itβs a visualization that helps understand the different levels of control and their interconnections in a manufacturing setting. The levels of the Automation | medium | 4,075 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
Pyramid, from bottom to top, typically include: Level 0: Field Devices and Instruments: This is the lowest level of the pyramid, where physical field devices such as sensors, actuators, and instruments are located. These devices gather data from the manufacturing process and send it to higher | medium | 4,076 |
Smart Manufacturing, Emqx, Internet of Things, Mqtt.
levels for processing, and control machinery. Level 1: Control Devices and PLCs (Programmable Logic Controllers): At this level, basic control functions are executed. PLCs and control devices receive input from field devices and make decisions based on pre-programmed logic. They control processes | medium | 4,077 |
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