Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications

In this paper, we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression C 4 - A 4 XB 4 where X is a variant quaternion matrix subject to quaternion matrix equations A 1 X = C 1 , XB 2 = C 2 , A 3 XB 3 = C 3 . As applications, we give a new necessary and sufficie...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 195; no. 2; pp. 733 - 744
Main Authors: Wang, Qing-Wen, Yu, Shao-Wen, Lin, Chun-Yan
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.02.2008
Elsevier
Subjects:
Algebra
Exact sciences and technology
Finite differences and functional equations
Generalized inverse
Linear and multilinear algebra, matrix theory
Linear matrix expression
Mathematical analysis
Mathematics
Maximal rank
Minimal rank
Numerical analysis
Numerical analysis. Scientific computation
Schur complement
Sciences and techniques of general use
System of quaternion matrix equations
System of quaternion matrix equations
Linear matrix expression
Maximal rank
Schur complement
Generalized inverse
Minimal rank
Numerical analysis
Necessary and sufficient condition
Existence of solution
Applied mathematics
Matrix equation
Equation system
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression C 4 - A 4 XB 4 where X is a variant quaternion matrix subject to quaternion matrix equations A 1 X = C 1 , XB 2 = C 2 , A 3 XB 3 = C 3 . As applications, we give a new necessary and sufficient condition for the existence of solutions to the system of matrix equations A 1 X = C 1 , XB 2 = C 2 , A 3 XB 3 = C 3 , A 4 XB 4 = C 4 , which was investigated by Wang [Q.W. Wang, A system of four matrix equations over von Neumann regular rings and its applications, Acta Math. Sin., 21(2) (2005) 323–334], by rank equalities. In addition, extremal ranks of the generalized Schur complement D - CA - B with respect to an inner inverse A − of A, which is a common solution to quaternion matrix equations A 1 X = C 1 , XB 2 = C 2 , are also considered. Some previous known results can be viewed as special cases of the results of this paper.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.05.018