Quick ways to _verify_ determinant, minimal polynomial, characteristic polynomial, eigenvalues, eigenvectors ...

Solution 1:

You can use the Caley-Hamilton theorem. Put your matrix in the characteristic polynomial and you should find $0$. Explicitly, $\chi_A(A) = A^n + a_{n-1}A^{n-1}+\cdots + a_0I=0$. This checks the
characteristic polynomial, the minimal polynomial and the eigenvalues. The only thing not checked is the dimension of the eigenspace, and the eigenvectors.

Of course this checking is simple, if your software computes matrix algebra.

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