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

### Summary

Summary: 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.

15A18, 65F15

### Keywords/Phrases

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