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- from sympy.core import symbols, S
- from sympy.functions import adjoint, conjugate, transpose
- from sympy.matrices.expressions import MatrixSymbol, Adjoint, trace, Transpose
- from sympy.matrices import eye, Matrix
- n, m, l, k, p = symbols('n m l k p', integer=True)
- A = MatrixSymbol('A', n, m)
- B = MatrixSymbol('B', m, l)
- C = MatrixSymbol('C', n, n)
- def test_adjoint():
- Sq = MatrixSymbol('Sq', n, n)
- assert Adjoint(A).shape == (m, n)
- assert Adjoint(A*B).shape == (l, n)
- assert adjoint(Adjoint(A)) == A
- assert isinstance(Adjoint(Adjoint(A)), Adjoint)
- assert conjugate(Adjoint(A)) == Transpose(A)
- assert transpose(Adjoint(A)) == Adjoint(Transpose(A))
- assert Adjoint(eye(3)).doit() == eye(3)
- assert Adjoint(S(5)).doit() == S(5)
- assert Adjoint(Matrix([[1, 2], [3, 4]])).doit() == Matrix([[1, 3], [2, 4]])
- assert adjoint(trace(Sq)) == conjugate(trace(Sq))
- assert trace(adjoint(Sq)) == conjugate(trace(Sq))
- assert Adjoint(Sq)[0, 1] == conjugate(Sq[1, 0])
- assert Adjoint(A*B).doit() == Adjoint(B) * Adjoint(A)
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