## 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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