Generic symmetric matrix pencils with bounded rank

Autor:	De Terán, Fernando, Dmytryshyn, Andrii, Dopico, Froilán M.
Rok vydání:	2018
Předmět:	Mathematics - Spectral Theory 15A22 15A18 15A21 65F15
Druh dokumentu:	Working Paper
Popis:	We show that the set of $n \times n$ complex symmetric matrix pencils of rank at most $r$ is the union of the closures of $\lfloor r/2\rfloor +1$ sets of matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of $n \times n$ complex symmetric matrix pencils of rank at most $r$. We also show that these closures correspond to the irreducible components of the set of $n\times n$ symmetric matrix pencils with rank at most $r$ when considered as an algebraic set. Comment: 15 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1808.03118 Zobrazit plný text záznamu View this record from Arxiv