Perturbation of multipleeigenvalues of Hermitian matrices (CROSBI ID 174311)
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Podaci o odgovornosti
Li, Ren-Cang ; Nakatsukasa, Yuji ; Truhar, Ninoslav ; Wang, Wei-guo
engleski
Perturbation of multipleeigenvalues of Hermitian matrices
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.
Graded perturbation; multiple eigenvalue; generalized eigenvalue problem
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Podaci o izdanju
437 (1)
2012.
202-213
objavljeno
0024-3795
10.1016/j.laa.2012.01.035