Generic symmetric matrix pencils with bounded rank
2020 (English)In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 10, no 3, p. 905-926Article in journal (Refereed) Published
Abstract [en]
We show that the set of n x n complex symmetric matrix pencils of rank at most r is the union of the closures of left perpendicular r/2 Right perpendicular + 1 sets of matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of n x n complex symmetric matrix pencils of rank at most r. We also show that the irreducible components of the set of n x n symmetric matrix pencils with rank at most r, when considered as an algebraic set, are among these closures.
Place, publisher, year, edition, pages
EMS Publishing House , 2020. Vol. 10, no 3, p. 905-926
Keywords [en]
Matrix pencil, symmetric pencil, strict equivalence, congruence, orbit, bundle, spectral information, complete eigenstructure
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-87325DOI: 10.4171/JST/316ISI: 000581041700006Scopus ID: 2-s2.0-85090910343OAI: oai:DiVA.org:oru-87325DiVA, id: diva2:1500164
Note
Funding Agencies:
Ministerio de Economia y Competitividad of Spain MTM2015-65798-P
Ministerio de Ciencia, Innovacion y Universidades of Spain MTM2017-90682-REDT
Agencia Estatal de Investigacion of Spain PID2019-106362GB-I00 / AEI / 10.13039/501100011033
2020-11-112020-11-112020-11-11Bibliographically approved