Solving a System of Sylvester-like Quaternion Matrix Equations
Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an applica...
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| Published in | Symmetry (Basel) Vol. 14; no. 5; p. 1056 |
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| Format | Journal Article |
| Language | English |
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| Abstract | Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the η-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper. |
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| AbstractList | Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the η-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper. |
| Author | Wang, Qing-Wen Liu, Long-Sheng Wang, Ruo-Nan |
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| Cites_doi | 10.1142/S1005386716000092 10.1007/s00006-017-0803-1 10.1080/03081087.2013.839667 10.1142/S0219530520400084 10.3390/math10101730 10.3390/sym14030550 10.1016/j.laa.2012.07.049 10.1007/s10957-021-01906-y 10.1016/j.laa.2003.12.039 10.1016/j.sigpro.2009.11.031 10.1016/S0252-9602(08)60019-3 10.1016/0024-3795(80)90189-5 10.1007/s40314-022-01873-8 10.1016/j.sysconle.2004.07.002 10.1016/0024-3795(79)90004-1 10.1016/j.sigpro.2010.06.024 10.1016/j.aml.2011.04.038 10.1080/03081087408817070 10.1137/151005907 10.1007/s00006-019-1038-0 10.1080/03081087.2011.648635 10.1109/TNN.2002.1031938 10.1016/j.laa.2021.08.015 10.1016/j.sigpro.2004.04.001 10.1016/j.automatica.2018.12.001 10.1016/j.cam.2021.113494 10.1016/j.automatica.2016.02.024 10.1080/03081087.2019.1633993 10.3390/sym14020375 |
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| SubjectTerms | Algebra Algorithms Control theory Mathematical analysis Moore-Penrose inverse quaternion matrix Quaternions rank Sylvester-type matrix equation η-Hermitian matrix |
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