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- from sympy.core import Basic
- from sympy.functions import adjoint, conjugate
- from sympy.matrices.expressions.transpose import transpose
- 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_conjugate(self):
- return transpose(self.arg)
- def _eval_trace(self):
- from sympy.matrices.expressions.trace import Trace
- return conjugate(Trace(self.arg))
- def _eval_transpose(self):
- return conjugate(self.arg)
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