Let A = XYT , where X is an m r matrix, YT is an r n matrix, and XTX and YT Y are both

Chapter 7, Problem 16

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Let A = XYT , where X is an m r matrix, YT is an r n matrix, and XTX and YT Y are both nonsingular. Show that the matrix B = Y(YT Y) 1 (XTX) 1 XT satisfies the Penrose conditions and hence must equal A+. Thus A+ can be determined from any factorization of this form.

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