On additive decompositions of solutions of the matrix equation \(AXB=C\)
type: Item
instance of: scholarly article
title: On additive decompositions of solutions of the matrix equation \(AXB=C\)
zbMATH Open document ID: 1214.15009
author: Yongge Tian
published in: Calcolo
publication date: 2010-12-03T00:00:00Z
review text: The author considers the triple of matrix equations \(AXB=C\) and \(A_iX_iB_i=C_i\), \(i=1,2\). He studies the possible presentation (when the consistency conditions are met) of the solution \(X\) to the first one as a sum of the solutions \(X_i\) to the last two of them. Applications are given on additive decompositions of generalized inverses and of decompositions of matrix equations into sums of solutions to their small equations.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5822855
zbMATH Keywords: matrix equation
zbMATH Keywords: general solution
zbMATH Keywords: additive decomposition of solution
zbMATH Keywords: set inclusion
zbMATH Keywords: generalized (Moore-Penrose) inverse
zbMATH Keywords: rank formulas for partitioned matrices
zbMATH Keywords: consistency conditions
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: s10092-010-0019-4
OpenAlex ID: W2014301771
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DOI: 10.1007/S10092-010-0019-4
description: scientific article; zbMATH DE number 5822855