Question: Problem 1. (10 points) Let A E Mmm(C) be a rank r matrix with the singular value decomposition A = UEV as in Theorem 6.27.

Problem 1. (10 points) Let A E Mmm(C) be a rank r matrix with the singular value decomposition A = UEV\" as in Theorem 6.27. Denote by 11.1,. . . ,um and '01, . . . , on the columns of U and V, respectively. Show that 'l" 1 * AT : Z gvjuj, i=1 3 where 01, . . . , or are the positive singular values

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