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.© BrainMass Inc. brainmass.com March 4, 2021, 7:00 pm ad1c9bdddf
Normal Matrices and Eigenpairs are investigated. The solution is detailed and well presented.