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 …

Bundles of matrix pencils (under strict equivalence) are sets of pencils having the same
Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbits …

We determine the generic complete eigenstructures for n*n complex symmetric matrix
polynomials of odd grade d and rank at most r. More precisely, we show that the set of n*n …

We give new proofs of several known results about perturbations of matrix pencils. In
particular, we give a direct and constructive proof of Andrzej Pokrzywa's theorem (1983), in …

The generic change of the Weierstraß canonical form of regular complex structured matrix
pencils under generic structure-preserving additive low-rank perturbations is studied …

Versal deformation of a matrix A is a normal form to which all matrices A+ E, close to A, can
be reduced by similarity transformation smoothly depending on the entries of A+ E. In this …

Bundles of matrix polynomials are sets of matrix polynomials with the same size and grade
and the same eigenstructure up to the specific values of the eigenvalues. It is known that the …

The paper considers the study of linearization techniques of cubic two-parameter matrix
polynomial (CTMP). We analyze vector spaces of linearization of CTMP, namely ansatz …

A number of theoretical and computational problems for matrix polynomials are solved by
passing to linearizations. Therefore a perturbation theory, that relates perturbations in the …

The quartic eigenvalue problem (λ4 A+ λ3 B+ λ2 C+ λ D+ E) x= 0 naturally arises in a
plethora of applications, such as when solving the Orr–Sommerfeld equation in the stability …