Matrix majorization via vector majorization

For two real m×n matrices X and Y, Y is said to majorize X if SY=X for some doubly stochastic matrix S of order m. In this note, we prove that Y majorizes X if and only if Y v majorizes X v for every real n-vector v , under the assumption that [X, e ][Y, e ] + is nonnegative, where e and [Y, e ] + d...

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Bibliographic Details
Published in:Linear algebra and its applications 2001-08, Vol.332, p.15-21
Main Authors: Hwang, Suk-Geun, Pyo, Sung-Soo
Format: Article
Language:English
Subjects:
Doubly stochastic marix
Matrix majorization
Vector majorization
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Summary:For two real m×n matrices X and Y, Y is said to majorize X if SY=X for some doubly stochastic matrix S of order m. In this note, we prove that Y majorizes X if and only if Y v majorizes X v for every real n-vector v , under the assumption that [X, e ][Y, e ] + is nonnegative, where e and [Y, e ] + denote the m-vector of ones and the Moore–Penrose generalized inverse of [Y, e ] , respectively.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00069-0