On Sylvester's law of inertia for nonlinear eigenvalue problems : dedicated to Lothar Reichel on the occasion of his 60th birthday
For Hermitian matrices and generalized definite eigenproblems, the LDLH 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. Copyright © 2013, Kent State University.
Sylvester's law of inertia