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General Information
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2014Vol.4(4): 273-277 ISSN: 2010-3697
DOI: 10.7763/IJMO.2014.V4.385

On Solvents of Matrix Polynomials

Malika Yaici and Kamel Hariche

Abstract—This paper is concerned with the construction of right and left solvents (also called block roots) of a matrix polynomial from latent roots and vectors. It addresses also the important case of the existence of a complete set of block roots. Solvents do not always exist, so conditions for the existence of such solvents are discussed. The inverse of a matrix polynomial is obtained as a particular case of the block partial fraction expansion of a related rational matrix. It involves the knowledge of a complete set of solvents and the computation of the inverse of a block Vandermonde matrix. Numerical examples are given to illustrate the two results.

Index Terms—Block partial fraction expansion, latent roots, latent vectors, matrix fraction description, matrix polynomials, solvents.

M. Yaici is with the Computer Department, University of Bejaia, Bejaia 06000, Algeria (e-mail: yaici_m@ hotmail.com).
K. Hariche is with Electronics and Electronics Institute, University of Boumerdes, Boumerdes 35000, Algeria (e-mail: khariche@yahoo.com).


Cite: Malika Yaici and Kamel Hariche, "On Solvents of Matrix Polynomials," International Journal of Modeling and Optimization vol. 4, no. 4, pp. 273-277, 2014.

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