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(Spectral Factorization) Suppose a 3 × 3 matrix A admits a factorization as A = PDP−1, where P is some invertible 3 × 3 matrix and D is the diagonal matrix
Show that this factorization is useful when computing high powers of A. Find fairly simple formulas for A2, A3, and Ak (k a positive integer), using P and the entries in D.
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Linear Algebra and Its Applications (5th Edition)
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