Numerical enclosure for multiple eigenvalues of an Hermitian matrix whose graph is a tree
نویسندگان
چکیده
منابع مشابه
On the Multiplicities of Eigenvalues of a Hermitian Matrix Whose Graph Is a Tree
A different approach is given to recent results due mainly to R.C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The technics developed are based on some results of matchings polynomials and use a work by O.L. Heilmann and E.H. Lieb on an apparently unrelated topic.
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We extend some interlacing properties of the eigenvalues of tridiagonal matrices to Hermitian matrices whose graph is a tree. We also give a graphical interpretation of the results. We use the work on matchings polynomials by O.L. Heilmann and E.H. Lieb.
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The eigenvalues of a Hermitian matrix function that depends on one parameter analytically can be ordered so that each eigenvalue is an analytic function of the parameter. Ordering these analytic eigenvalues from the largest to the smallest yields continuous and piece-wise analytic functions. For multi-variate Hermitian matrix functions that depend on d parameters analytically, the ordered eigen...
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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: 2009
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.06.038