We introduce a new family of strong linearizations of matrix polynomials—which we call
“block Kronecker pencils”—and perform a backward stability analysis of complete …

We prove that we can always construct strongly minimal linearizations of an arbitrary rational
matrix from its Laurent expansion around the point at infinity, which happens to be the case …

We develop a complete and rigorous theory of root polynomials of arbitrary matrix
polynomials, ie, either regular or singular, and study how these vector polynomials are …

Regular and singular matrix polynomials P (λ)=∑ i= 0 k P i ϕ i (λ), P i∈ R n× n given in an
orthogonal basis ϕ 0 (λ), ϕ 1 (λ),…, ϕ k (λ) are considered. Following the ideas in [9], the …

We start by introducing a new class of structured matrix polynomials, namely, the class of
$\mathbf {M} _A $-structured matrix polynomials, to provide a common framework for many …

We construct a new family of strong linearizations of rational matrices considering the
polynomial part of them expressed in a basis that satisfies a three term recurrence relation …

In this paper, we introduce a new family of equations for matrix pencils that may be utilized
for the construction of strong linearizations for any square or rectangular matrix polynomial …

A complete theory of the relationship between the minimal bases and indices of rational
matrices and those of their strong linearizations is presented. Such theory is based on …

The standard way of solving a polynomial eigenvalue problem associated with a matrix
polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil …

Polynomial minimal bases of rational vector subspaces are a classical concept that plays an
important role in control theory, linear systems theory, and coding theory. It is a common …