The concept of linearization is fundamental for theory, applications, and spectral
computations related to matrix polynomials. However, recent research on several important …

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 discuss Möbius transformations for general matrix polynomials over arbitrary fields,
analyzing their influence on regularity, rank, determinant, constructs such as compound …

We present necessary and sufficient conditions for the existence of a matrix polynomial
when its degree, its finite and infinite elementary divisors, and its left and right minimal …

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 …

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 …

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 …

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 …