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This routine solves the (ordinary) eigenvalue problem for a complex
hermitian square matrix A. Given A, an unitary matrix Q is calculated which
diagonalizes A:

    Q' A Q = diag(E)               and                Q Q' = Q' Q = 1

Here diag(E) a is diagonal matrix whose diagonal is E.
' denotes the hermitian transpose (i.e. ordinary transposition and
complex conjugation).

src/s/y/sympy-0.7.5/sympy/mpmath/tests/test_eigen_symmetric.py   sympy(Download)
def run_eighe(A, verbose = False):
    if verbose:
        print("original matrix:\n", str(A))
    D, Q = mp.eighe(A)