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The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).


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The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).

a) If two square matrices are similar, show that they have the same characteristic polynomials.

b) Conversely, if two matrices have the same characteristic polynomials, are they similar? Proof or counterexample.
in Mathematics by ♦ Platinum (97.7k points) | 346 views

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