5 papers
Generic eigenstructures of Hermitian pencils
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We obtain the generic complete eigenstructures of complex Hermitian matrix pencils with rank at most (with ). To do this, we prove that the set of such pen…
Generic symmetric matrix polynomials with bounded rank and fixed odd grade
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We determine the generic complete eigenstructures for complex symmetric matrix polynomials of odd grade and rank at most . More precisely, we show that the set…
Low rank perturbation of regular matrix pencils with symmetry structures
Fernando De Terán, Christian Mehl, Volker Mehrmann
The generic change of the Weierstrass Canonical Form of regular complex structured matrix pencils under generic structure-preserving additive low-rank perturbations is studied. Sev…
Generic symmetric matrix pencils with bounded rank
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
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,…
An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank
Fernando De Terán, Froilán M. Dopico, J. M. Landsberg
The set of mxn singular matrix pencils with normal rank at most r is an algebraic set with r+1 irreducible components. These components are the closure of the orbits (under strict…