Speaker
Description
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 under strict equivalence). The notion of a bundle for matrix pencils was introduced in the 1990's, following the same notion for matrices under similarity, introduced by Arnold in 1971, and it has been extensively used since then.
During my talk we will describe the closure of the bundle of a pencil L, denoted by B(L), as the union of B(L) itself with a finite number of other bundles, where the dimension of each of these bundles is strictly smaller than the dimension of B(L).
For this reason we derive a formula for the (co)dimension of the bundle of a matrix pencil in terms of the Weyr characteristics of the partial multiplicities of the eigenvalues and of the (left and right) minimal indices. The talk is based on papers:
[1] F. De Teran and F. M. Dopico, On bundles of matrix pencils under strict equivalence, Linear Algebra Appl., 658 (2023), pp. 1–31.
[2] F. De Teran, F. M. Dopico, V. Koval and P.Pagacz, On bundles closures of matrix pencils and matrix polynomials, Annali della Scuola normale superiore di Pisa - Classe di scienze, 2024.
