For a positive integer n and for a real number s, let s n denote the set of all n ร n real matrices whose rows and columns have sum s. In this note, by an explicit constructive method, we prove the following. (i) Given any real n-tuple = (ฮป 1 , ฮป 2 , . . . , ฮป n ) T , there exists a symmetric matri
Inequalities for the spectra of symmetric doubly stochastic matrices
โ Scribed by Rajesh Pereira; Mohammad Ali Vali
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 106 KB
- Volume
- 419
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let S denote either the set of n ร n symmetric doubly stochastic matrices or the set of n ร n symmetric doubly substochastic matrices and let T be a linear map on span S. We prove that T (S) = S if and only if there exists an n ร n permutation matrix P such that T (X) = P t XP for all X โ span S. Ou
In this paper, we study the region s n of R n where the decreasingly ordered spectra of all the nรn symmetric doubly stochastic matrices lie with emphasis on the boundary set of s n . As applications, we study the case n = 4 and in particular we solve the inverse eigenvalue problem for 4ร4 symmetric