A Cramer rule for finding the solution of a class of singular equations
type: Item
instance of: scholarly article
title: A Cramer rule for finding the solution of a class of singular equations
zbMATH Open document ID: 0671.15006
DOI: 10.1016/0024-3795(89)90395-9
author: Guo-rong Wang
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: Let A be an \(n\times n\) complex matrix and let k be the least nonnegative integer such that rank \(A^ k=rank A^{k+1}\). If b is in the range of \(A^ k\), then there is a unique x in the range of \(A^ k\) such that \(Ax=b\). The author obtains a Cramer's rule type result for finding this solution. The result reduces to the usual Cramer's rule for nonsingular A.
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 4097558
zbMATH Keywords: Drazin inverse
zbMATH Keywords: singular equations
zbMATH Keywords: rank
zbMATH Keywords: Cramer's rule
reviewed by: George Phillip Barker
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90395-9
OpenAlex ID: W2090847218
cites work: A Cramer rule for least-norm solutions of consistent linear equations
cites work: A ''Cramer rule'' for the least-norm, least-squared-error solution of inconsistent linear equations
cites work: A Cramer rule for minimum-norm (T) least-squares (S) solution of inconsistent linear equations
cites work: Q3207128
cites work: Q4061081
description: scientific article; zbMATH DE number 4097558