Normal Matrices - Texas A&M University

6.1. INTRODUCTION TO NORMAL MATRICES 199 Proof. (a) ⇒(b). If A is normal, then AA∗is Hermitian and therefore unitarily diagonalizable. Thus U∗A ∗AU = D = U∗AA∗U.Also,A, A , A ∗A = AA form a commuting family.This implies that eigenvectors of

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