In this problem we show that the eigenvalues of a Hermitian matrix A are real. Let x be
Chapter 7, Problem 27(choose chapter or problem)
In this problem we show that the eigenvalues of a Hermitian matrix A are real. Let x be an eigenvector corresponding to the eigenvalue . a. Show that (Ax, x) = (x, Ax). Hint: See 21c. b. Show that (x, x) = (x, x). Hint: Recall that Ax = x. c. Show that = ; that is, the eigenvalue is real. 2
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