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Removing zero rows of U leaves A = LU, where the r columns or L span the column space of
Chapter 6, Problem 6.3.21(choose chapter or problem)
Removing zero rows of U leaves A = LU, where the r columns or L span the column space of A and the r rows of U span the row space. Then A + has the explicit formula U T (U U T ) 1 (L TL) 1L T . Why is A +b in the row space with U T at the front? Why does A TAA+b = A Tb, so that x + = A +b satisfies the normal equation as it should?
Questions & Answers
QUESTION:
Removing zero rows of U leaves A = LU, where the r columns or L span the column space of A and the r rows of U span the row space. Then A + has the explicit formula U T (U U T ) 1 (L TL) 1L T . Why is A +b in the row space with U T at the front? Why does A TAA+b = A Tb, so that x + = A +b satisfies the normal equation as it should?
ANSWER:Step 1 of 5
Given that and the rows of span the row space of . So, the column of span the row space of .
Consider, the columns of by and the given explicit formula for is