- Journal of Spectral Theory Journal
- September 2020
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International Standard Serial Number (ISSN)
- We show that the set of n × n complex symmetric matrix pencils of rank at mostr 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 × ncomplex 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 whenconsidered as an algebraic set.
- matrix pencil; symmetric pencil; strict equivalence; congruence; orbit; bundle; spectral information; complete eigenstructure