If two $n \times n$ matrices have the same characteristic polynomials, determinant and trace, are they similar, EVEN if ($ \lnot \#Spec= 0$)?
2026-04-01 18:49:51.1775069391
If two matrices have the same characteristic polynomials, determinant and trace, are they similar?
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The answer is no. Take the identity matrix and the matrix $$a_{11}=a_{12}=a_{22}=1, a_{21}=0.$$