Geodesic
Sharp lower bounds for the dimension of linearizations of matrix polynomials
The electronic journal of linear algebra, Tome 17 (2008), pp. 518-531.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A standard way of dealing with matrix polynomial eigenvalue problems is to use linearizations. Byers, Mehrmann and Xu have recently defined and studied linearizations of dimensions smaller than the classical ones. In this paper, lower bounds are provided for the dimensions of linearizations and strong linearizations of a given m $\times n$ matrix polynomial, and particular linearizations are constructed for which these bounds are attained. It is also proven that strong linearizations of an n $\times n$ regular matrix polynomial of degree must have dimension n $\times n$ .
Classification : 15A18, 15A21, 15A22, 65F15
Keywords: matrix polynomials, matrix pencils, linearizations, dimension 
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     author = {De Teran, Fernando and Dopico, Froilan M.},
     title = {Sharp lower bounds for the dimension of linearizations of matrix polynomials},
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De Teran, Fernando; Dopico, Froilan M. Sharp lower bounds for the dimension of linearizations of matrix polynomials. The electronic journal of linear algebra, Tome 17 (2008), pp. 518-531. http://geodesic.mathdoc.fr/item/ELA_2008__17__a7/