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In Exercises 17–24, A is an m × n matrix with a singular value decomposition A = UΣVT, where U is an m × m orthogonal matrix, Σ is an m × n “diagonal” matrix with r positive entries and no negative entries, and V is an n × n orthogonal matrix. Justify each answer.
22. Show that if A is an n × n positive definite matrix, then an orthogonal diagonalization A = PDPT is a singular value decomposition of A.
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