—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.
—Block partial fraction expansion, latent roots,
latent vectors, matrix fraction description, matrix polynomials,
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: email@example.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.