A Sin 22 Theorem for Graded Indeenite Hermitian Matrices 1 Date and Revision Information Go Here a Sin 22 Theorem for Graded Indeenite Hermitian Matrices

This paper gives double angle theorems that bound the change in an invariant subspace of an inde nite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a de nite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only relative gaps and norms of A as in the de nite case but also norms of so-called the hyperbolic eigenvector matrices of certain associated matrix pairs. For two special but interest cases, bounds on these hyperbolic eigenvector matrices are obtained to show that their norms are of moderate magnitude. This report is available on the web at http://www.ms.uky.edu/~rcli/. 2(University Osijek, Croatia) Lehrgebiet Mathematische Physik, Fernuniversitat, 58084 Hagen Germany ([email protected]). 3Department of Mathematics, University of Kentucky, Lexington, KY 40506 ([email protected]). This work was supported in part by the National Science Foundation under Grant No. ACI-9721388 and by the National Science Foundation CAREER award under Grant No. CCR-9875201. A sin 2 Theorem for Graded Inde nite Hermitian Matrices Ninoslav Truhar Ren-Cang Li