Let, two symmetric real $n \times n$ matrices have the same minimal polynomial, are they similar?
I know that they are congruent, but are they also similar? If it's false, what is a counterexample?
2026-03-25 08:07:58.1774426078
Question about symmetric matrices and similarity
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$Diag(0,0,1)$ and $Diag(0,1,1)$ have the same minimal polynomial $X^2-X=0$, but not similar since they have different rank.