In Exercises 17–24, A is an m × n matrix with
Chapter 7, Problem 22E(choose chapter or problem)
In Exercises 17–24, A is an m × n matrix with a singular value decomposition , where U is an m × m orthogonal matrix, 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.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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