A representation of the general common solution to the matrix equations A(1)XB(1)=C-1 and A(2)XB(2)=C-2 with applications

Authors
Navarra, A Odell, PL Young, DM
Citation
A. Navarra et al., A representation of the general common solution to the matrix equations A(1)XB(1)=C-1 and A(2)XB(2)=C-2 with applications, COMPUT MATH, 41(7-8), 2001, pp. 929-935
Citations number
20
Categorie Soggetti
Computer Science & Engineering
Journal title
COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN journal
08981221 → ACNP
Volume
41
Issue
7-8
Year of publication
2001
Pages
929 - 935
Database
ISI
SICI code
0898-1221(200104)41:7-8<929:AROTGC>2.0.ZU;2-9
Abstract
We give new necessary and sufficient conditions for the existence of a comm on solution to the pair of linear matrix equations A(1)XB(1) = C-1 and A(2) XB(2) = C-2 and derive a new representation of the general common solution to these two equations. We apply this result to determine new necessary and sufficient conditions for the existence of an Hermitian solution and a rep resentation of the general Hermitian solution to the matrix equation AXE = C. (C) 2001 Elsevier Science Ltd. All rights reserved.