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Clandry
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Homework Statement
Consider an invertible n x n matrix A. Can you write A as A=LQ, where L is a lower triangular matrix and Q is orthogonal? Hint: Consider the QR factorization of #A^T#.
Homework Equations
For QR factorization, Q is orthogonal and R is upper triangular.
The Attempt at a Solution
If we consider the hint, then we can write:
##A^T=S*U## where S is orthogonal matrix and U is some upper triangular matrix.
##(A^T)^T=U^T*S^T##; transpose of upper triangular matrix U is some lower triangular matrix L
##A=L*S^T##
Here is where I get lost. I don't know how to show that S^T=Q. Could someone please give me a hint?
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