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.
19. Show that the columns of V are eigenvectors of AT A, the columns of U are eigenvectors of AAT, and the diagonal entries of Σ are the singular values of A. [Hint: Use the SVD to compute ATA and AAT.]
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