Structures and uniqueness conditions of \(MK\)-weighted pseudoinverses
type: Item
instance of: scholarly article
title: Structures and uniqueness conditions of \(MK\)-weighted pseudoinverses
zbMATH Open document ID: 0811.15003
DOI: 10.1007/BF01935652
author: Musheng Wei
author: Birong Zhang
published in: BIT
publication date: 1995-05-07T00:00:00Z
review text: For given matrices \(M\), \(A\) and \(K\), two kinds of \(MK\)-weighted pseudoinverses \(X\) of \(A\) are studied. The first kind is characterized by the following four conditions (similar to the Moore-Penrose conditions): \(MAXA = MA\), \(XAX = X\), \((M^ HMAX)^ H =M^ H MAX\), \((K^ H KXA)^ H =K^ HKXA\). The second kind is characterized by \[ \min_{X \in S} \| X \|_ K \quad \text{with} \quad S = \biggl\{ X : \| AX - I \|_ M = \min_{W \in C^{n \times s}} \| AW - I \|_ M \biggr\}. \] Structures of these \(MK\)-weighted pseudoinverses of \(A\) are deduced, and uniqueness conditions are obtained.
reviewed by: Giacomo Bonanno
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 698684
zbMATH Keywords: constrained least squares
zbMATH Keywords: weighted pseudoinverses
zbMATH Keywords: structures
zbMATH Keywords: Moore- Penrose conditions
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01935652
OpenAlex ID: W2001808243
description: scientific article; zbMATH DE number 698684