Prove that the eigenvalues of a and a t are identical prove, Computer Engineering

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Prove that the eigenvalues of a and a t are identical prove

Problem

1. Let Find all eigenvalues of M. Does M have two linearly independent eigenvectors?

2. Prove that the eigenvalues of A and A T are identical.

3. Prove that the eigenvalues of a diagonal matrix are equal to the diagonal elements.

4. Suppose that matrix A has an eigenvector v with eigenvalue λ. Show that v is also an eigenvector for A2, and find the corresponding eigenvalue. How about for Ak, for 2 ≤ k ≤ n?

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