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December 7th, 2012, 10:01 PM   #1
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Let X = [-1 3 0, 1 -1 4, 0 1 -1]. Find an orthogonal matrix K, a diagonal matrix A, and an upper triangular matrix N with 1's on the diagonal such that X=KAN. (Hint: Begin with the "QR-factorization" of X).

I figured out the QR-factorization and I got Q = [-1/sqrt(2) 1/sqrt(3) 1/sqrt(6), 1/sqrt(2) 1/sqrt(3) 1/sqrt(6), 0 1/sqrt(3) -2/sqrt(6)] and R = [2/sqrt(2) -4/sqrt(2) 4/sqrt(2), 0 3/sqrt(3) 3/sqrt(3), 0 0 6/sqrt(6)]. Please verify if my calculations were correct for QR.

This is how far I got but I don't know what to do next to figure out K, A, and N. Do you guys have any ideas how to figure this out?
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