منابع مشابه
Multiple Eigenvalues
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each corresponding codimension is the number of conditions which a matrix of the given type must satisfy in order to have the specified multiplicities.
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Let T be a tree of order n > 6 with μ as a positive eigenvalue of multiplicity k. Star complements are used to show that (i) if k > n/3 then μ = 1, (ii) if μ = 1 then, without restriction on k, T has k+ 1 pendant edges that form an induced matching. The results are used to identify the trees with a non-zero eigenvalue of maximum possible multiplicity.
متن کاملStructured Hölder Condition Numbers for Multiple Eigenvalues
The sensitivity of a multiple eigenvalue of a matrix under perturbations can be measured by its Hölder condition number. Various extensions of this concept are considered. A meaningful notion of structured Hölder condition numbers is introduced and it is shown that many existing results on structured condition numbers for simple eigenvalues carry over to multiple eigenvalues. The structures inv...
متن کاملComputational Error Bounds for Multiple or Nearly Multiple Eigenvalues
In this paper bounds for clusters of eigenvalues of non-selfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multiple eigenvalues, and for a basis of the corresponding invariant subspaces. The input matrix may be real or complex, dense or sparse. The method is based on a quadratically convergent Newton-like method; it in...
متن کاملPerturbation of Multiple Eigenvalues of Hermitian Matrices
This paper is concerned with the perturbation of a multiple eigenvalue μ of the Hermitian matrix A = diag(μI, A22) when it undergoes an off-diagonal Email addresses: [email protected] (Ren-Cang Li), [email protected] (Yuji Nakatsukasa), [email protected] (Ninoslav Truhar), [email protected] (Wei-guo Wang) Supported in part by National Science Foundation Grants DMS-0810506 and DMS1115...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.06.022