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 …

This paper defines for the first time strong linearizations of arbitrary rational matrices, studies
in depth properties and characterizations of such linear matrix pencils, and develops …

The standard way of solving the polynomial eigenvalue problem associated with a matrix
polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil …

The set POL d, rm× n of m× n complex matrix polynomials of grade d and (normal) rank at
most r in a complex (d+ 1) mn dimensional space is studied. For r= 1,…, min⁡{m, n}− 1, we …

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 …

We show that the set of m× m complex skew-symmetric matrix polynomials of odd grade d,
ie, of degree at most d, and (normal) rank at most 2r is the closure of the single set of matrix …

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 …

The structural data of any rational matrix R(λ), ie, the structural indices of its poles and zeros
together with the minimal indices of its left and right nullspaces, is known to satisfy a simple …

This paper studies generic and perturbation properties inside the linear space of m×(m+ n)
polynomial matrices whose rows have degrees bounded by a given list d 1,…, dm of natural …