Prove or give a counterexample: a.) A and AT have the same eigenvalues. b.) A and AT have the same eigenvectors.

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asked Aug 11, 2021 137k views

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Lixiang · Answer 1 · 2021-08-18T11:43:23+0000

Answer: Although A and AT have the same eigenvalues, they may actually have different eigenvectors for that particular eigenvalue. Therefore A and AT have at least one eigenvector that aren't in common.

Explanation:

These two attachment explains the provings and counterexamples briefly and simply

Prove or give a counterexample: a.) A and AT have the same eigenvalues. b.) A and-example-1

Prove or give a counterexample: a.) A and AT have the same eigenvalues. b.) A and-example-2

Prove or give a counterexample: a.) A and AT have the same eigenvalues. b.) A and AT have the same eigenvectors.

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