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from sympy.core import Basic
from sympy.functions import adjoint, conjugate
from sympy.matrices.expressions.matexpr import MatrixExpr
class Adjoint(MatrixExpr):
"""
The Hermitian adjoint of a matrix expression.
This is a symbolic object that simply stores its argument without
evaluating it. To actually compute the adjoint, use the ``adjoint()``
function.
Examples
========
>>> from sympy import MatrixSymbol, Adjoint, adjoint
>>> A = MatrixSymbol('A', 3, 5)
>>> B = MatrixSymbol('B', 5, 3)
>>> Adjoint(A*B)
Adjoint(A*B)
>>> adjoint(A*B)
Adjoint(B)*Adjoint(A)
>>> adjoint(A*B) == Adjoint(A*B)
False
>>> adjoint(A*B) == Adjoint(A*B).doit()
True
"""
is_Adjoint = True
def doit(self, **hints):
arg = self.arg
if hints.get('deep', True) and isinstance(arg, Basic):
return adjoint(arg.doit(**hints))
else:
return adjoint(self.arg)
@property
def arg(self):
return self.args[0]
@property
def shape(self):
return self.arg.shape[::-1]
def _entry(self, i, j, **kwargs):
return conjugate(self.arg._entry(j, i, **kwargs))
def _eval_adjoint(self):
return self.arg
def _eval_transpose(self):
return self.arg.conjugate()
def _eval_conjugate(self):
return self.arg.transpose()
def _eval_trace(self):
from sympy.matrices.expressions.trace import Trace
return conjugate(Trace(self.arg))
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