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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Vydáno v:	Applied mathematics and computation Ročník 195; číslo 2; s. 733 - 744
Hlavní autoři:	Wang, Qing-Wen, Yu, Shao-Wen, Lin, Chun-Yan
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY Elsevier Inc 01.02.2008 Elsevier
Témata:	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
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Popis
Shrnutí:	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