Euclidean and circum-Euclidean distance matrices: Characterizations and linear preservers
نویسندگان
چکیده
منابع مشابه
Euclidean and circum-Euclidean distance matrices: Characterizations and linear preservers
Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.
متن کاملEla Euclidean and Circum-euclidean Distance Matrices: Characterizations and Linear Preservers
Short proofs are given to various characterizations of the (circum-)Euclidean squared distance matrices. Linear preserver problems related to these matrices are discussed.
متن کاملOn Euclidean distance matrices
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...
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...
متن کاملProperties of Euclidean and Non-Euclidean Distance Matrices
A distance matrix D of order n is symmetric with elements idfj, where d,, = 0. D is Euclidean when the in(n 1) quantities dij can be generated as the distances between a set of n points, X (n X p), in a Euclidean space of dimension p. The dimensionality of D is defined as the least value of p = rank(X) of any generating X; in general p + 1 and p +2 are also acceptable but may include imaginary ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2010
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1406