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In this paper we consider Rellich's diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigen-values of hyperbolic operator polynomials.
A pair of matrices is said to be imbeddable precisely when one is an isometric projection of the other on a suitable subspace. The concept of imbedding has been the subject of extensive study. Particular emphasis has been placed on relating the spectra of the matrices involved, especially when both matrices are Hermitian or normal. In this paper, the notion… (More)