Naslov
Perturbation of multipleeigenvalues of Hermitian matrices

Autori
Li, Ren-Cang ; Nakatsukasa, Yuji ; Truhar, Ninoslav ; Wang, Wei-guo

Izvornik
Linear algebra and its applications (0024-3795) 437 (2012), 1; 202-213

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Graded perturbation; multiple eigenvalue; generalized eigenvalue problem

Sažetak
This paper is concerned with the perturbation of the multiple eigenvalue $\mu$ of Hermitian matrices of the form $A=\mbox{; ; ; ; diag}; ; ; ; (\mu I, A_{; ; ; ; 22}; ; ; ; )$, when the matrix undergoes an off-diagonal perturbation $E$ whose columns have widely varying magnitudes. When some of $E$'s columns are much smaller than the others, some copies of $\mu$ are much insensitive than any existing bound suggests. We explain this phenomenon by showing that when $A_{; ; ; ; 22}; ; ; ; -\mu I$ is definite the $i$th bound scales quadratically with the norm of the $i$th column, and in the indefinite case the bound is necessarily proportional to the product of $E$'s $i$th column norm and $E$'s norm. An extension to generalized Hermitian eigenvalue problems is presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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