Completing triangular block matrices with maximal and minimal ranks
type: Item
instance of: scholarly article
title: Completing triangular block matrices with maximal and minimal ranks
zbMATH Open document ID: 0984.15013
DOI: 10.1016/S0024-3795(00)00224-X
author: Yongge Tian
published in: Linear Algebra and its Applications
publication date: 2002-05-07T00:00:00Z
review text: The author considers two completion problems on block matrices with maximal and minimal ranks: For \(A=(A_{ij})\) an \(n\times n\) block matrix, where \(A_{ij}\) \((n\geq i\geq j\geq 1)\) is given, and \(A_{ij}\) \((1\leq i<j \leq n)\) is a variant block entity, determine all these variant block entries such that \(A=(A_{ij})\) has maximal and minimal possible rank, respectively. By using the theory of generalized inverses of matrices, the author presents complete solutions to these two problems. As applications he also determines maximal and minimal ranks of the matrix expression \(A-B\times C\) when \(X\) is a variant triangular block matrix, then presents a necessary and sufficient condition for the matrix equation \(B\times C=A\) to have a triangular block solution.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 1563497
zbMATH Keywords: matrix completion
zbMATH Keywords: block matrices
zbMATH Keywords: maximal and minimal ranks
zbMATH Keywords: generalized inverses
zbMATH Keywords: matrix equation
reviewed by: Takayuki Nôno
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563497