A note on subset selection for matrices
type: Item
instance of: scholarly article
title: A note on subset selection for matrices
zbMATH Open document ID: 1221.15030
published in: Linear Algebra and its Applications
publication date: 2011-03-17T00:00:00Z
full work available at URL: a-note-on-subset-selection-for-matrices(5f86d83c-ffcd-438e-8e9b-7e3e73c1d620).html
review text: The problem of selecting rows of a matrix \(X\) so that the resulting matrix \(A\) is ``as non-singular as possible'' is considered: given \(X\in\mathbb{R}^{m\times n}\) with \(n<m\) and rank\,\(X=n\), determine a permutation matrix \(P\in\mathbb{R}^{n\times n}\) so that \[ PX=\left[\begin{matrix} A\\B\end{matrix}\right],\;A\in\mathbb{R}^{k\times n},\;\text{rank\,}A=n,\;n\leq k<m. \] Upper bounds for \(\|A^+\|_F\) (where \(A^+\) is the Moore-Penrose inverse of \(A\)) and the singular values of \(A\) have been obtained by the authors in a previous paper. These results are improved in the present paper by providing a constructive derivation for the bounds of \(\|A^+\|_F\) and new lower bounds for \(\det A^TA\).
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 5867182
zbMATH Keywords: permutation matrix
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: singular values
zbMATH Keywords: overdetermined
zbMATH Keywords: Frobenius norm
zbMATH Keywords: determinant
zbMATH Keywords: rank
zbMATH Keywords: lower bounds
author: F. R. De Hoog
author: R. M. M. Mattheij
MaRDI profile type: Publication
OpenAlex ID: W2114983089
cites work: Q4633910
cites work: Handbook series linear algebra. Linear least squares solutions by Householder transformations
cites work: Subset selection for matrices
cites work: Q5185900
cites work: Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
cites work: Q3922026
DOI: 10.1016/J.LAA.2010.11.053
description: scientific article; zbMATH DE number 5867182