Question

Prove or give a counterexample:

a.) A and AT have the same eigenvalues.
b.) A and AT have the same eigenvectors.

Answer 1

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