The Euclidean distance matrix for distinct points in โ is generically of rank + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case = 1 is generically .
On the diagonal scaling of Euclidean distance matrices to doubly stochastic matrices
โ Scribed by Charles R. Johnson; Robert D. Masson; Michael W. Trosset
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 220 KB
- Volume
- 397
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
For n 3 6, we determine the minimum permanents and minimizing matrices on the faces of R3+,, the polytope of (3 + n) x (3 + n) doubly stochastic matrices. whose nonzero entries coincide with those of where J is the matrix with all entries equal 1, I the identity matrix, and 0 the zero matrix.
We consider the minimum permanents and minimising matrices on the faces of the polytope of doubly stochastic matrices whose nonzero entries coincide with those of, respectively, . Here J r,s denotes the r ร s matrix all of whose entries are 1, I n is the identity matrix of order n and 0 m is the m