RT Journal Article
T1 On bundles of matrix pencils under strict equivalence
A1 Terán Vergara, Fernando de
A1 Martínez Dopico, Froilán César
AB 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 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. Despite the amount of literature devoted to describing the topology of bundles of matrix pencils, some relevant questions remain still open in this context. For example, the following two: (a) provide a characterization for the inclusion relation between the closures (in the standard topology) of bundles; and (b) are the bundles open in their closure? The main goal of this paper is providing an explicit answer to these two questions. In order to get this answer, we also review and/or formalize some notions and results already existing in the literature. We also prove that bundles of matrices under similarity, as well as bundles of matrix polynomials (defined as the set of m x n  matrix polynomials of the same grade having the same spectral information, up to the eigenvalues) are open in their closure.
PB Elsevier
SN 0024-3795
YR 2023
FD 2023-02-01
LK https://hdl.handle.net/10016/36669
UL https://hdl.handle.net/10016/36669
LA eng
NO This work has been supported by the Agencia Estatal de Investigación of Spain through grants PID2019-106362GB-I00 MCIN/ AEI/10.13039/501100011033/ and MTM2017-90682-REDT, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
DS e-Archivo
RD 1 sept. 2024