Re: LQ Decomposition and Null Space

From: pa@xxxxxxxxxxxxxxxxxxxxx (Pierre Asselin)
Date: Sat, 31 Mar 2007 14:50:49 +0000 (UTC)

michael@xxxxxxxxxxxxxxxx wrote:

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
.

References:
- LQ Decomposition and Null Space
  - From: michael

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Null Space
... Given a matrix Awhere m<=n, LAPACK subroutine DGELQF calculates ... the LQ decomposition A=Q where Land Q. ... DORGLQ forms the first m rows of the matrix Q. These rows correspond ...
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LQ Decomposition and Null Space
... Given a matrix Awhere m<=n, LAPACK subroutine DGELQF calculates ... the LQ decomposition A=Q where Land Q. ... DORGLQ forms the first m rows of the matrix Q. These rows correspond ...
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