Normalized Frobenius condition number of the orthogonal projections of the identity
type: Item
instance of: scholarly article
title: Normalized Frobenius condition number of the orthogonal projections of the identity
zbMATH Open document ID: 1263.15004
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2013-03-11T00:00:00Z
review text: The authors deal with the orthogonal projection \(AN\) (in the Frobenius sense) of the identity matrix \(I\) onto the matrix subspace \(AS\) (\(A\in \mathbb R^{n\times n}\), \(S\) being an arbitrary subspace of \(\mathbb R^{n\times n}\)). Lower and upper bounds on the normalized Frobenius condition number of the matrix \(AN\) are given. Further, for every matrix subspace \(S\subset \mathbb R^{n\times n}\), a new index \(\hat k_F(A,S)\), which generalizes the normalized Frobenius condition number of the matrix \(A\), is defined and analyzed.
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 6143230
zbMATH Keywords: Frobenius norm minimization
zbMATH Keywords: orthogonal projections
zbMATH Keywords: Frobenius condition number
reviewed by: Costică Moroşanu
MaRDI profile type: Publication
full work available at URL: j.jmaa.2012.11.021
OpenAlex ID: W2085422628
DOI: 10.1016/J.JMAA.2012.11.021
description: scientific article; zbMATH DE number 6143230