Article ID Journal Published Year Pages File Type
9498549 Linear Algebra and its Applications 2005 12 Pages PDF
Abstract
We consider the problem of scaling a nondegenerate predistance matrix A to a doubly stochastic matrix B. If A is nondegenerate, then there exists a unique positive diagonal matrix C such that B = CAC. We further demonstrate that, if A is a Euclidean distance matrix, then B is a spherical Euclidean distance matrix. Finally, we investigate how scaling a nondegenerate Euclidean distance matrix A to a doubly stochastic matrix transforms the points that generate A. We find that this transformation is equivalent to an inverse stereographic projection.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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