Ranks and the least-norm of the general solution to a system of quaternion matrix equations

We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations A 1 X 1 = C 1 , A 2 X 2 = C 2 , A 3 X 1 B 1 + A 4 X 2 B 2 = C 3 , which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew)symmetric common soluti...

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Vydáno v:	Linear algebra and its applications Ročník 430; číslo 5; s. 1626 - 1640
Hlavní autoři:	Wang, Qing-Wen, Li, Cheng-Kun
Médium:	Journal Article Konferenční příspěvek
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Inc 01.03.2009 Elsevier
Témata:	Algebra Exact sciences and technology Least-norm Linear and multilinear algebra, matrix theory Linear matrix expression Mathematics Maximal rank Minimal rank Moore–Penrose inverse Sciences and techniques of general use System of quaternion matrix equations System of quaternion matrix equations 15A24 Moore–Penrose inverse Linear matrix expression 15A33 Minimal rank 15A03 Least-norm 15A60 Maximal rank 15A09 Antisymmetric matrix Operator equation Moore Penrose inverse Quaternion Normed space Generalized inverse Moore-Penrose inverse Linear system Matrix inversion Ring Matrix equation Normed algebra
ISSN:	0024-3795
On-line přístup:	Získat plný text
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Shrnutí:	We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations A 1 X 1 = C 1 , A 2 X 2 = C 2 , A 3 X 1 B 1 + A 4 X 2 B 2 = C 3 , which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew)symmetric common solutions to a pair of quaternion matrix equations, Appl. Math. Comput. 195 (2008) 721–732], then derive the maximal and minimal ranks and the least-norm of the general solution to the system mentioned above. Some previous known results can be viewed as special cases of the results of this paper.
ISSN:	0024-3795
DOI:	10.1016/j.laa.2008.05.031