Gershgorin theory for the generalized eigenvalue problem 𝐴𝑥=𝜆𝐵𝑥

Abstract

A generalization of Gershgorin’s theorem is developed for the eigenvalue problem A x = λ B x Ax = \lambda Bx and is applied to obtain perturbation bounds for multiple eigenvalues. The results are interpreted in terms of the chordal metric on the Riemann sphere, which is especially convenient for treating infinite eigenvalues.