The `QR` factorization with column pivoting does not enable us to compute
a *minimum norm* solution to a rank-deficient linear least squares problem,
unless . However,
by applying further orthogonal (or unitary) transformations
from the right to the upper trapezoidal matrix
,
using the routine xTZRQF, can be eliminated:

This gives the
**complete orthogonal
factorization**

from which the minimum norm solution can be obtained as

Tue Nov 29 14:03:33 EST 1994