Geodesic
Double angle theorems for definite matrix pairs
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 33-57.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 15A15, 15A09, 15A23
Keywords: matrix pairs, perturbation of eigenvectors, $\sin 2 \theta$ theorems 
@article{ETNA_2016__45__a23,
     author = {Grubi\v{s}i\'c, Luka and Miodragovi\'c, Suzana and Truhar, Ninoslav},
     title = {Double angle theorems for definite matrix pairs},
     journal = {Electronic transactions on numerical analysis},
     pages = {33--57},
     publisher = {mathdoc},
     volume = {45},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a23/}
}
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Grubišić, Luka; Miodragović, Suzana; Truhar, Ninoslav. Double angle theorems for definite matrix pairs. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 33-57. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a23/