Citation:
De Terán, F., Dmytryshyn, A. & Dopico, F. (2020). Generic symmetric matrix pencils with bounded rank. Journal of Spectral Theory, 10(3), pp. 905–926.
xmlui.dri2xhtml.METS-1.0.item-contributor-funder:
Ministerio de Economía y Competitividad (España) Ministerio de Ciencia, Innovación y Universidades (España)
Project:
Gobierno de España. MTM2015-65798-P Gobierno de España. MTM2017-90682-REDT
We show that the set of n × n complex symmetric matrix pencils of rank at most r is the union of the closures of [r/2] + 1 sets of matrix pencils with some, explicitly described,complete eigenstructures. As a consequence, these are the generic complete eigenstWe show that the set of n × n complex symmetric matrix pencils of rank at most r is the union of the closures of [r/2] + 1 sets of matrix pencils with some, explicitly described,complete eigenstructures. As a consequence, these are the generic complete eigenstructures of n × n complex symmetric matrix pencils of rank at most r. We also show that these closures correspondto the irreducible components of the set of n × n symmetric matrix pencils with rank at most r when considered as an algebraic set.[+][-]