Volume 45, pp. 33-57, 2016.

Double angle theorems for definite matrix pairs

Luka Grubišić, Suzana Miodragović, and Ninoslav Truhar

Abstract

In this paper we present new double angle theorems for the rotation of the eigenspaces of Hermitian matrix pairs $(H,M)$, where $H$ is a non-singular matrix which can be factorized as $H = G J G^*$, $J = diag(\pm 1),$ and $M$ is non-singular. The rotation of the eigenspaces is measured in the matrix-dependent scalar product, and the bounds belong to relative perturbation theory. The quality of the new bounds are illustrated in the numerical examples.

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Key words

matrix pairs, perturbation of eigenvectors, $\sin 2 \Theta$ theorems

AMS subject classifications

15A15, 15A09, 15A23

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