Let A be a 5 5 matrix with real entries. Let A = QT QT be the real Schur decomposition

Chapter 6, Problem 19

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Let A be a 5 5 matrix with real entries. Let A = QT QT be the real Schur decomposition of A, where T is a block matrix of the form given in equation (2). What are the possible block structures for T in each of the following cases? (a) All of the eigenvalues of A are real. (b) A has three real eigenvalues and two complex eigenvalues. (c) A has one real eigenvalue and four complex eigenvalues. 2

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