Generic symmetric matrix pencils with bounded rank

  • Fernando De Terán

    Universidad Carlos III de Madrid, Spain
  • Andrii Dmytryshyn

    Örebro University, Sweden
  • Froilán M. Dopico

    Universidad Carlos III de Madrid, Leganés, Spain
Generic symmetric matrix pencils with bounded rank cover

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Abstract

We show that the set of complex symmetric matrix pencils of rank at most is the union of the closures of sets of matrix pencils with some, explicitly described, complete eigenstructures. As a consequence, these are the generic complete eigenstructures of complex symmetric matrix pencils of rank at most . We also show that the irreducible components of the set of symmetric matrix pencils with rank at most , when considered as an algebraic set, are among these closures.

Cite this article

Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico, Generic symmetric matrix pencils with bounded rank. J. Spectr. Theory 10 (2020), no. 3, pp. 905–926

DOI 10.4171/JST/316