Special generalized inverse matrices connected with the theory of unified least squares
type: Item
instance of: scholarly article
title: Special generalized inverse matrices connected with the theory of unified least squares
zbMATH Open document ID: 0887.15023
DOI: 10.1016/S0024-3795(95)07778-2
published in: Linear Algebra and its Applications
publication date: 1998-01-28T00:00:00Z
review text: Let the symbols \(A^T\), \(A^-\) and \(R(A)\) denote the transpose, any generalized inverse, and the range of \(A\in \mathbb{R}^{m \times n}\) respectively; \((A:B)\) denotes the partitioned matrix composed from the matrices \(A\) and \(B\) that have the same number of rows. In this paper, for a nonnegative definite matrix \(V\) and a matrix \(X\) with the same number of rows, it is demonstrated how to obtain explicit matrices \(G\) such that the range \(R(X:V) =R(V+ XGG^TX^T)\) and \(V(V+ XGG^TX^T)^- V=V\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1076298
zbMATH Keywords: unified least squares
zbMATH Keywords: generalized inverse
zbMATH Keywords: nonnegative definite matrix
zbMATH Keywords: range
author: Jürgen Gross
reviewed by: Jule Zhang
MaRDI profile type: Publication
cites work: Strong unified-least-squares matrices for a general linear model
cites work: Q4050723
cites work: Unified Least Squares Approach to Linear Estimation in a General Gauss–Markov Model
cites work: Q5646256
cites work: Unified theory of least squares
cites work: Least squares theory for possibly singular models
cites work: Q5645536
full work available at URL: s0024-3795(95)07778-2
OpenAlex ID: W2145220971
description: scientific article; zbMATH DE number 1076298