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Let $$A=\pmatrix{0&0&0\cr 1&0&0\cr 1&1&0}.$$
The eigenvalues of A+A^*$A+A^T$
(q=0) are 2,-1,-1. The eigenvalues of
-A-A^*$-A-A^T$ (q=\piq=$\pi$) are
-2,1,1.
Let $$A=\pmatrix{0&0&0\cr 1&0&0\cr 1&1&0}.$$
The eigenvalues of A+A^*
(q=0) are 2,-1,-1. The eigenvalues of
-A-A^* (q=\pi) are
-2,1,1.
Let $$A=\pmatrix{0&0&0\cr 1&0&0\cr 1&1&0}.$$
The eigenvalues of $A+A^T$
(q=0) are 2,-1,-1. The eigenvalues of
$-A-A^T$ (q=$\pi$) are
-2,1,1.
