Suppose ˆA is the triangular matrix we obtained after the Householder transformation, ˆA=ˆQˆU, and multiply from the left with ˆQ−1 resulting in ˆQ−1ˆA=ˆU. Suppose that ˆQ consists of a series of planar Jacobi like rotations acting on sub blocks of ˆA so that all elements below the diagonal are zeroed out ˆQ=ˆR12ˆR23…ˆRn−1,n.