Generic eigenstructures of Hermitian pencils

2022/09/21 by De Terán, Fernando, Dmytryshyn, Andrii, Dopico, Froilán M. · 4 citations
#15A18 #15A21 #15A22 #15A54 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2209.10495

Abstract

We obtain the generic complete eigenstructures of complex Hermitian n× n matrix pencils with rank at most r (with r≤ n). To do this, we prove that the set of such pencils is the union of a finite number of bundle closures, where each bundle is the set of complex Hermitian n× n pencils with the same complete eigenstructure (up to the specific values of the finite eigenvalues). We also obtain the explicit number of such bundles and their codimension. The cases r=n, corresponding to general Hermitian pencils, and r

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