On group inverse of singular Toeplitz matrices
type: Item
instance of: scholarly article
title: On group inverse of singular Toeplitz matrices
zbMATH Open document ID: 1072.15007
author: Huai-An Diao
author: Yimin Wei
published in: Linear Algebra and its Applications
publication date: 2005-04-21T00:00:00Z
review text: The paper deals with representations of the group inverses of real singular Toeplitz matrices. The authors study the group inverse of the following \((n+1) \times (n+1)\) real singular Toeplitz matrix \[ M= \left[ \begin{matrix} A & c \\ b^T & d \end{matrix} \right], \] where \(A\) ia a real \(n \times n\) singular Toeplitz matrix, \(b\) and \(c\) are real \(1 \times n\) vectors and \(b^T\) denotes the transpose of \(b\). The main result of this paper is to show that if \(A\) and \(M\), in the previous expression, are singular matrices and have index one, then the group inverse of \(M\) can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes the matrix representation of the inverse known as ``Gohberg-Semencul formula''.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 2160183
zbMATH Keywords: group inverse
zbMATH Keywords: index
zbMATH Keywords: real singular Toeplitz matrices
zbMATH Keywords: matrix representation
zbMATH Keywords: Gohberg-Semencul formula
reviewed by: Juan Ramón Torregrosa Sánchez
MaRDI profile type: Publication
full work available at URL: j.laa.2004.08.021
OpenAlex ID: W2044120295
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DOI: 10.1016/J.LAA.2004.08.021
description: scientific article; zbMATH DE number 2160183