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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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