Naslov
The tan Θ theorem for definite matrix pairs

Autori
Ivičić, Ivana Kuzmanović ; Miodragović, Suzana ; Ugrica, Matea

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Linear and Multilinear Algebra (2022)

Status rada
Poslan

Ključne riječi
perturbation of matrix pairs ; rotation of subspaces ; tangent theta theorem

Sažetak
In this paper, we consider the perturbation of a Hermitian matrix pair $(H, M)$, where $H$ and $M$ are non-singular and positive definite Hermitian matrices, respectively. A novel upper bound on a tangent of the angles between the eigenspaces of perturbed and unperturbed pairs is derived under a perturbation to the off-diagonal blocks of $H$. The rotation of the eigenspaces under a perturbation is measured in the matrix-dependent scalar product. We show that a $\tan\Theta$ bound for the standard eigenvalue problem is a special case of our new bound and that the obtained bound can be much sharper than the existing $\sin\Theta$ bounds.

Izvorni jezik
Engleski

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