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Previous issue date: 2015-10-29 === Esse trabalho de pesquisa tem por objetivo, fazer um estudo sobre a teoria alg?brica dos polin?mios matriciais m?nicos, bem como das defini??es, conceitos e propriedades de no que diz respeito a bloco autovalores, bloco autovetores e solventes de P(X). Investigando as principais rela??es entre o polin?mio matricial e as matrizes bloco. Companheira e bloco Vandermonde. Estudamos a constru??o de polin?mios matriciais com determinados solventes e a extens?on da M?todo da Pot?ncia , para calcular blocos autovalores da matriz Companheira e solventes de P(X). Atrav?s da rela??o entre o bloco autovalor dominante da matriz Companheira e o solvente dominante de P(X) ? poss?vel obtermos a converg?ncia do algoritmo para o solvente dominante do polin?mio matricial m?nico. Ilustramos com exemplos num?ricos para casos distintos de converg?ncia. === This research work aims to make a study of the algebraic theory of matrix monic
polynomials, as well as the definitions, concepts and properties with respect to block
eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations
between the matrix polynomial and the Companion and Vandermonde matrices. We study
the construction of matrix polynomials with certain solvents and the extention of the Power
Method, to calculate block eigenvalues and solvents of P(X). Through the relationship
between the dominant block eigenvalue of the Companion matrix and the dominant solvent of
P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the
matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.
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