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### Other Factorizations

The QL and RQ factorizations are given by
and
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 [5].

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