On the explicit solutions of forms of the Sylvester and the Yakubovich matrix equations

Ramadan, M.A. ; Abdel Naby, M.A. ; Bayoumi, A.M.E. 


Abstract


In this paper, we consider the explicit solutions of two matrix equations, namely, the Yakubovich matrix equation V - A V F = B W and Sylvester matrix equations A V - E V F = B W, A V + B W = E V F and A V - V F = B W. For this purpose, we make use of Kronecker map and Sylvester sum as well as the concept of coefficients of characteristic polynomial of the matrix A. Some lemmas and theorems are stated and proved where explicit and parametric solutions are obtained. The proposed methods are illustrated by numerical examples. The results obtained show that the methods are very neat and efficient. © 2009 Elsevier Ltd. All rights reserved.


Other data

Issue Date 2009
Journal Mathematical and Computer Modelling 
URI http://research.asu.edu.eg/123456789/548
DOI 9-10
1400
http://www.scopus.com/inward/record.url?eid=2-s2.0-70349456522&partnerID=MN8TOARS
50
10.1016/j.mcm.2009.07.008


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