trix(a) # what happens if input is a matrix object
>>> A
matrix([[ 1.+0.j, -0.-2.j],
        [ 0.+2.j,  5.+0.j]])
>>> eigenvalues, eigenvectors = LA.eigh(A)
>>> eigenvalues
array([0.17157288, 5.82842712])
>>> eigenvectors
matrix([[-0.92387953+0.j        , -0.38268343+0.j        ], # may vary
        [ 0.        +0.38268343j,  0.        -0.92387953j]])

>>> # demonstrate the treatment of the imaginary part of the diagonal
>>> a = np.array([[5+2j, 9-2j], [0+2j, 2-1j]])
>>> a
array([[5.+2.j, 9.-2.j],
       [0.+2.j, 2.-1.j]])
>>> # with UPLO='L' this is numerically equivalent to using LA.eig() with:
>>> b = np.array([[5.+0.j, 0.-2.j], [0.+2.j, 2.-0.j]])
>>> b
array([[5.+0.j, 0.-2.j],
       [0.+2.j, 2.+0.j]])
>>> wa, va = LA.eigh(a)
>>> wb, vb = LA.eig(b)
>>> wa
array([1., 6.])
>>> wb
array([6.+0.j, 1.+0.j])
>>> va
array([[-0.4472136 +0.j        , -0.89442719+0.j        ], # may vary
       [ 0.        +0.89442719j,  0.        -0.4472136j ]])
>>> vb
array([[ 0.89442719+0.j       , -0.        +0.4472136j],
       [-0.        +0.4472136j,  0.89442719+0.j       ]])

rB