The `LQ`**factorization**
is given by

where `L` is `m`-by-`m` lower triangular, `Q` is `n`-by-`n`
orthogonal (or unitary), consists of the first `m` rows of `Q`,
and the remaining `n` - `m` rows.

This factorization is computed by the routine xGELQF, and again `Q` is
represented as a product of elementary reflectors; xORGLQ
(or xUNGLQ in the complex case) can generate
all or part of `Q`, and xORMLQ (or xUNMLQ
) can pre- or post-multiply a given
matrix
by `Q` or ( if `Q` is complex).

The `LQ` factorization of `A` is essentially the same as the `QR` factorization
of ( if `A` is complex), since

The `LQ` factorization may be used to find a minimum norm solution of
an underdetermined system of linear equations `Ax` = `b` where `A` is
`m`-by-`n` with `m` < `n` and has rank `m`. The solution is given by

and may be computed by calls to xTRTRS and xORMLQ.

Tue Nov 29 14:03:33 EST 1994