Suppose you have a factorization A QR into an orthogonal ma

Suppose you have a factorization A = QR into an orthogonal matrix Q and an upper triangular matrix R. Is there another factorization A = Q\'R\' with Q notequalto Q\' and R notequalto R! with the same properties?

Solution

YES

If A is invertible, then the factorization is unique otherwise it may have more than 1 factorization.

for more details you can read \"QR decomposition\" on wikipedia.