A note on the boundary of the set where the decreasingly ordered spectra of symmetric doubly stochastic matrices lie
✍ Scribed by Bassam Mourad
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 172 KB
- Volume
- 416
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
In this paper, we study the region s n of R n where the decreasingly ordered spectra of all the n×n 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 4×4 symmetric doubly stochastic matrices of trace zero by using different techniques than that used in [H. Perfect, L. Mirsky, Spectral properties of doubly stochastic matrices, Monatsh. Math. 69 (1965) 35-57]. Also, we solve the same problem for 4×4 symmetric doubly stochastic matrices of trace two which serves only to illustrate this paper's method. In addition, we describe a nonconvex region E f of s 4 which corresponds to new sufficient conditions for the 4×4 symmetric doubly stochastic matrices. At the end, we conjecture that E f = s 4 .