The QL and RQ factorizations
are given by
These factorizations are computed by PxGEQLF and PxGERQF, respectively; they are less commonly used than either the QR or LQ factorizations described above, but have applications in, for example, the computation of generalized QR factorizations .
All the factorization routines discussed here (except PxTZRZF) allow arbitrary m and n, so that in some cases the matrices R or L are trapezoidal rather than triangular. A routine that performs pivoting is provided only for the QR factorization.
Table 3.7: Computational routines for orthogonal factorizations