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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| Published in: | Linear algebra and its applications Vol. 430; no. 5; pp. 1626 - 1640 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Wang, Qing-Wen Li, Cheng-Kun |
| Author_xml | – sequence: 1 givenname: Qing-Wen surname: Wang fullname: Wang, Qing-Wen email: wqw858@yahoo.com.cn – sequence: 2 givenname: Cheng-Kun surname: Li fullname: Li, Cheng-Kun |
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| Cites_doi | 10.1080/03081087408817070 10.1080/0308108031000114631 10.1016/j.amc.2007.08.091 10.1016/0024-3795(87)90217-5 10.1016/j.amc.2007.05.021 10.1016/S0024-3795(02)00345-2 10.1016/j.camwa.2006.05.011 10.1016/j.laa.2003.12.039 10.1016/S0024-3795(03)00420-8 10.1016/0024-3795(84)90166-6 10.1016/j.amc.2007.05.018 10.1016/0024-3795(90)90377-O 10.1016/j.amc.2006.12.039 10.1080/03081080008818664 10.1016/j.amc.2006.06.012 |
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| Keywords | 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 |
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| Snippet | 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
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| SubjectTerms | 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 |
| Title | Ranks and the least-norm of the general solution to a system of quaternion matrix equations |
| URI | https://dx.doi.org/10.1016/j.laa.2008.05.031 |
| Volume | 430 |
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