Generic eigenstructure of Hermitian pencils

We obtain the generic complete eigenstructures of complex Hermitian nxn 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 nxn pencils with the same complete eigenstructure (up to the specific values of the distinct 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

Generic eigenstructure of Hermitian pencils Articles