A Householder transform is a method used to transform an mxn matrix A of rank n into an mxn upper triangular matrix R by successive pre-multiplications of A with the Householder matrices Hi, where i = 1, 2, ..., k, and k=min(m-1, n): Ak = R = Hk Hk-1 ... H1 A0, with A0 = A and Ai = Hi Ai-1,