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Vector majorization via positive definite matrices

โœ Scribed by Richard A. Brualdi; Suk-Geun Hwang; Sung-Soo Pyo

Book ID
104155921
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
460 KB
Volume
257
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

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 characterize when there is a positive definite doubly stochastic matrix A such that Ay = x.

๐Ÿ“œ SIMILAR VOLUMES

Majorization via generalized Hessenberg
Majorization via generalized Hessenberg matrices
โœ Suk-Geun Hwang ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 157 KB

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