## On Sylvester's law of inertia for nonlinear eigenvalue problems

Aleksandra Kostić and Heinrich Voss

### Abstract

For Hermitian matrices and generalized definite eigenproblems, the $LDL^H$ factorization provides an easy tool to slice the spectrum into two disjoint intervals. In this note we generalize this method to nonlinear eigenvalue problems allowing for a minmax characterization of (some of) their real eigenvalues. In particular we apply this approach to several classes of quadratic pencils.

Full Text (PDF) [151 KB], BibTeX

### Key words

eigenvalue, variational characterization, minmax principle, Sylvester's law of inertia

15A18, 65F15

### Links to the cited ETNA articles

 [18] Vol. 36 (2009-2010), pp. 113-125 Markus Stammberger and Heinrich Voss: On an unsymmetric eigenvalue problem governing free vibrations of fluid-solid structures

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