廣義特徵值問題之研究

Abstract

The localization of eigenvalues of the generalized eigenproblem Ax=λBx,where A and B are M matrices, is studied in this paper.We show that all eigenvalues of the aboue problem lie in an annulus centered at the origin in the complex plane, and the inner and outer radii of the annulus depend only on the moduli of the entries of the matrices A and B.Moreover, a detailed study of eigenvalues appearing on the boundary of the annulus is also being made.