Concern an m x n matrix A with a reduced singular value decomposition, A = U r

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Concern an m x n matrix A with a reduced singular value decomposition, A = UDVrT, and the pseudoinverse A+ = Vr D–1UTr.

Verify the properties of A+:

a. For each y in Rm, AA+y is the orthogonal projection of y onto Col A.

b. For each x in Rn, A+Ax is the orthogonal projection of x onto Row A.

c. AA+A = A and A+ AA= A+.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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