Author: Pierre AsselinPierre Asselin Date: Mar 31, 2007 07:50
> Given a matrix A(m,n) where m<=n, LAPACK subroutine DGELQF calculates
> the LQ decomposition A=(L 0)Q where L(m,m) and Q(n,n). The subroutine
> DORGLQ forms the first m rows of the matrix Q. These rows correspond
> to the Transpose(Range) space of the matrix A. The null space
> transpose corresponds to the n-m rows of Q. Does anyone know of an
> efficient way to form this null space?
See the part on Householder matrices in section 5.2 of Gilbert
Strang, "Introduction to Applied Mathematics", starting on p. 392
(Wellesley-Cambridge Press 1985, ISBN 0-9614088-0-4). It gives an
LQ decomposition (QR, actually, but take the transpose) with a
square matrix Q, including your missing rows.
I don't know if there is a Lapack for that.
--
pa at panix dot com
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