Vector Majorization Via Hessenberg Matrices | Zendy

Brualdi Richard A. | Zendy; Hwang SukGeun | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Vector Majorization Via Hessenberg Matrices

Author(s) -

Brualdi Richard A.,

Hwang SukGeun

Publication year - 1996

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/53.1.28

Subject(s) - majorization , combinatorics , permutation matrix , mathematics , permutation (music) , regular polygon , matrix (chemical analysis) , physics , chemistry , geometry , chromatography , circulant matrix , acoustics

In this paper it is proved that, for real n ‐vectors x and y, x is majorized by y if and only if x = PHQ y for some permutation matrices P, Q , and for some doubly stochastic matrix H which is a direct sum of doubly stochastic Hessenberg matrices. This result reveals that any n ‐vector which is majorized by a vector y can be expressed as a convex combination of at most ( n 2 − n + 2)/2 permutations of y.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research