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A c ombination of Sylvester block sum and block matrix Kronecker map for explicit solutions of Sylvester system of matrix equations
Author(s) -
Ramadan Mohamed A.,
Bayoumi Ahmed M.E.,
Hadhoud Adel R.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5875
Subject(s) - kronecker product , mathematics , sylvester matrix , sylvester equation , matrix (chemical analysis) , block matrix , kronecker delta , block (permutation group theory) , sylvester's law of inertia , combinatorics , matrix polynomial , algebra over a field , polynomial matrix , polynomial , symmetric matrix , pure mathematics , mathematical analysis , eigenvalues and eigenvectors , quantum mechanics , composite material , physics , materials science
In this paper, we consider an explicit solution of system of Sylvester matrix equations of the form A 1 V 1 − E 1 V 1 F 1 = B 1 W 1 and A 2 V 2 − E 2 V 2 F 2 = B 2 W 2 with F 1 and F 2 being arbitrary matrices, where V 1 , W 1 , V 2 and W 2 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.