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 = Ur DVrT, 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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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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