Majorization for the eigenvalues of Euclidean distance matrices
نویسندگان
چکیده
منابع مشابه
On the eigenvalues of Euclidean distance matrices
In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and non-spherical centrally symmetric EDMs. The paper also presents methods for constructing cospectral EDMs and EDMs with exactly three distinct eigenvalues. Mathematical subject classif...
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We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a compact set Ωn of R. Under various assumptions we establish the almost sure convergence of the limiting spectral measure as the number of points goes to infinity. The moments of the limiting distribution are computed, and we prove that t...
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If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of PAP . As an application, we obtain a formula for the MoorePenrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which w...
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We present an efficient algorithm to find a realization of a (full) n × n squared Euclidean distance matrix in the smallest possible dimension. Most existing algorithms work in a given dimension: most of these can be transformed to an algorithm to find the minimum dimension, but gain a logarithmic factor of n in their worstcase running time. Our algorithm performs cubically in n (and linearly w...
متن کاملEuclidean Distance Matrices and Applications
Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of res...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.08.022