A combination of Sylvester block sum and block matrix Kronecker map for explicit solutions of Sylvester system of matrix equations
Ramadan, Mohamed A.; Bayoumi, Ahmed M. E.; Hadhoud, Adel R.;
Abstract
In this paper, we consider an explicit solution of system of Sylvester matrix equations of the form A1V1 − E1V1F1 = B1W1 and A2V2 − E2V2F2 = B2W2 with F1 and F2 being arbitrary matrices, where V1,W1,V2 and W2 are the matrices to be determined. First, the definitions, of the matrix polynomial of block matrix, Sylvester sum, and Kronecker product of block matrices are defined. Some definitions, lemmas, and theorems that are needed to propose our method are stated and proved. Numerical test problems are solved to illustrate the suggested technique.
Other data
Title | A combination of Sylvester block sum and block matrix Kronecker map for explicit solutions of Sylvester system of matrix equations | Authors | Ramadan, Mohamed A.; Bayoumi, Ahmed M. E. ; Hadhoud, Adel R. | Keywords | degree of freedom;explicit solutions;Kronecker map;Sylvester matrix equations;Sylvester sum | Issue Date | 1-Dec-2019 | Publisher | WILEY | Journal | Mathematical Methods in the Applied Sciences | Volume | 42 | Issue | 18 | Start page | 7506 | End page | 7516 | ISSN | 01704214 | DOI | 10.1002/mma.5875 | Scopus ID | 2-s2.0-85070713799 | Web of science ID | WOS:000480221200001 |
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