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Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix.

a. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n

b. Prove that ( λ, x) is an eigenpair of A if (λ, x) is an eigenpair of A*. (Hence A and A* have the same eigenvectors.

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