The Spectral Variation of Pencils of Matrices

Abstract

Perturbation theorems for the spectrum of a regular matrix pencil $λA-B$ are given. As it may include points near or at infinity the Euclidean distance is not appropriate. We use the chordal metric and the distances. For those purpose we develop here an algebraic treatment of matrix pairs, with special reference to diagonable and definite pairs, using ideas from the theory of matrix polynomials.