منابع مشابه
Eigenvector Distribution of Wigner Matrices
We consider N×N Hermitian or symmetric random matrices with independent entries. The distribution of the (i, j)-th matrix element is given by a probability measure νij whose first two moments coincide with those of the corresponding Gaussian ensemble. We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees ...
متن کاملNonlinear eigenvalue { eigenvector problems for STP matrices
A matrix A is said to be strictly totally positive (STP) if all its minors are strictly positive. STP matrices were independently introduced by Schoenberg in 1930 (see [13, 14]) and by Krein and Gantmacher in the 1930s. The main results concerning eigenvalues and eigenvectors of STP matrices were proved by Gantmacher and Krein in their 1937 paper [6]. (An announcement appeared in 1935 in [5]. C...
متن کاملEigenvector Statistics of Sparse Random Matrices
We prove that the bulk eigenvectors of sparse random matrices, i.e. the adjacency matrices of ErdősRényi graphs or random regular graphs, are asymptotically jointly normal, provided the averaged degree increases with the size of the graphs. Our methodology follows [6] by analyzing the eigenvector flow under Dyson Brownian motion, combining with an isotropic local law for Green’s function. As an...
متن کاملHermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components
Given an n-by-n Hermitian matrix A and a real number λ, index i is said to be Parter (resp. neutral, downer) if the multiplicity of λ as an eigenvalue of A(i) is one more (resp. the same, one less) than that in A. In case the multiplicity of λ in A is at least 2 and the graph of A is a tree, there are always Parter vertices. Our purpose here is to advance the classification of vertices and, in ...
متن کاملThe Inverse Eigenvector Problem for Real Tridiagonal Matrices
A little known property of a pair of eigenvectors (column and row) of a real tridiagonal matrix is presented. With its help we can define necessary and sufficient conditions for the unique real tridiagonal matrix for which an approximate pair of complex eigenvectors are exact. Similarly we can designate the unique real tridiagonal matrix for which two approximate real eigenvectors, with differe...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)80019-5