4. The QR Decomposition and Least Squares
G. W. Stewart · Society for Industrial and Applied Mathematics eBooks · 1998
A useful approach to solving matrix problems is to ask what kinds of transformations preserve the solution and then use the transformations to simplify the problem. For example, the solution of the system Ax=b is not changed when the system is pre-multiplied by a nonsingular matrix. If we premultiply by elementary lower triangular matrices to reduce A to upper triangular form, the result is Gaussian elimination — as we saw in §1.1, Chapter 3.