On scaled projections and pseudoinverses
type: Item
instance of: scholarly article
title: On scaled projections and pseudoinverses
zbMATH Open document ID: 0658.15003
DOI: 10.1016/0024-3795(89)90594-6
author: G. W. Stewart
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Let X be a matrix of full column rank and let D be a diagonal matrix with positive diagonal elements. The weighted pseudoinverse of X is defined by \(X^+_ D=(X^ tDX)^{-1}X^ tD\) and the associated oblique projection is defined by \(P_ D=XX^+_ D\). The author proves that there is a positive number c which is independent of D such that \(\| P_ D\| \leq c\) and \(\| X^+_ D\| \leq c\| X^+\|\).
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 4075275
zbMATH Keywords: norm of matrix
zbMATH Keywords: weighted pseudoinverse
reviewed by: Shaokuan Li
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90594-6
OpenAlex ID: W2077875563
cites work: Q4089657
cites work: Robust Statistics
cites work: A new polynomial-time algorithm for linear programming
cites work: Q5753446
description: scientific article; zbMATH DE number 4075275