Question: Let A be a nilpotent matrix (see Exercise 56 in Section 4.2). Prove that there is an orthogonal matrix Q such that QT AQ is

Let A be a nilpotent matrix (see Exercise 56 in Section 4.2). Prove that there is an orthogonal matrix Q such that QT AQ is upper triangular with zeros on its diagonal. [Hint: Use Exercise 27.]

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