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.
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