If AAA is a m×nm \times nm×n matrix; Ax=bA\mathbf{x} = \mathbf{b}Ax=b is an inconsistent system and has a least-square solution x^\hat{\mathbf{x}}x^.
b−Ax^\mathbf{b} - A\hat{\mathbf{x}}b−Ax^ is always in Nul ATA^TAT.
