Majorization permutahedra and -matrices
โ Scribed by Geir Dahl
- Book ID
- 104038245
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 137 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Several classes of substochastic matrices are introduced in higher dimensions, and some theorems about their extreme points are presented. An extension of a theorem of von Neumann concerning doubly substochastic matrices is discussed, and the classes for which this extension remains valid are determ
In this paper we give a method of constructing generalized Hessenberg matrices from those of smaller orders, with a simple combinatorial justiยฎcation. Making use of this construction, we also prove that, for real n-vectors x and y whose components are arranged in nonincreasing order, x is majorized
It is well known that for real n-vectors y and x, y majorizes x if and only if Ay = x for some doubly stochastic matrix A of order n. If the components of each of y and x are in nonincreasing order, then it is known that the mat~x A can be chosen to be positive semidefinite symmetric. We characteriz