# Numerical Linear Algebra : Normal Matrices and Eigenpairs

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

a. Prove that A - M is normal for any Î» âˆˆ C. Prove that ||Ax||2 - ||âˆ§*x||2 for all x âˆˆ C^n

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

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#### Solution Summary

Normal Matrices and Eigenpairs are investigated. The solution is detailed and well presented.

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