Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498549 | Linear Algebra and its Applications | 2005 | 12 Pages |
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 BÂ =Â 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
Authors
Charles R. Johnson, Robert D. Masson, Michael W. Trosset,