describe how to find the general solution of the matrix equation XA+ AXT= 0, with A∈ Cn× n,
which allows us to determine the dimension of its solution space. This result has immediate …

We show that perturbations of polynomial matrices of full normal-rank can be analyzed via
the study of perturbations of companion form linearizations of such polynomial matrices. It is …

We study how small perturbations of a skew-symmetric matrix pencil may change its
canonical form under congruence. This problem is also known as the stratification problem …

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

We study how small perturbations of general matrix polynomials may change their
elementary divisors and minimal indices by constructing the closure hierarchy (stratification) …

We study how elementary divisors and minimal indices of a skew-symmetric matrix
polynomial of odd degree may change under small perturbations of the matrix coefficients …

Matlab functions to work with the canonical structures for congruence and* congruence of
matrices, and for congruence of symmetric and skew-symmetric matrix pencils are …

We construct the Hasse diagrams G 2 and G 3 for the closure ordering on the sets of
congruence classes of 2× 2 and 3× 3 complex matrices. In other words, we construct two …

The homogeneous system of matrix equations (XTA+ AX, XTB+ BX)=(0, 0), where (A, B) is a
pair of skew-symmetric matrices of the same size is considered: we establish the general …

In this paper we give a complete description of the possible feedback invariants of a pair of
matrices submitted to an additive perturbation of low rank. Also, we describe the possible …