Majorization for matrix classes

Geir Dahl; Alexander Guterman; Pavel Shteyner

doi:10.1016/j.laa.2018.06.003

Majorization for matrix classes

Geir Dahl, Alexander Guterman, Pavel Shteyner

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We introduce a new majorization order for classes (sets) of matrices which generalizes several existing notions of matrix majorization. Roughly, the notion says that every matrix in one class is majorized by some matrix in the other class. The motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments. This connection is briefly described. We investigate properties of this new order both of algebraic and geometric character. In particular, we establish results on so-called minimal cover classes with respect to the introduced majorization.

Original language	English
Pages (from-to)	201-221
Number of pages	21
Journal	Linear Algebra and Its Applications
Volume	555
DOIs	https://doi.org/10.1016/j.laa.2018.06.003
State	Published - 15 Oct 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Funding

The investigations of the second and the third authors were financially supported by RSF grant 16-11-10075.

Funders	Funder number
Russian Science Foundation	16-11-10075

Keywords

Doubly stochastic matrix
Matrix majorization
Partial order

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10.1016/j.laa.2018.06.003

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AU - Guterman, Alexander

AU - Shteyner, Pavel

PY - 2018/10/15

Y1 - 2018/10/15

N2 - We introduce a new majorization order for classes (sets) of matrices which generalizes several existing notions of matrix majorization. Roughly, the notion says that every matrix in one class is majorized by some matrix in the other class. The motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments. This connection is briefly described. We investigate properties of this new order both of algebraic and geometric character. In particular, we establish results on so-called minimal cover classes with respect to the introduced majorization.

AB - We introduce a new majorization order for classes (sets) of matrices which generalizes several existing notions of matrix majorization. Roughly, the notion says that every matrix in one class is majorized by some matrix in the other class. The motivation to study this majorization concept comes from mathematical statistics and involves the information content in experiments. This connection is briefly described. We investigate properties of this new order both of algebraic and geometric character. In particular, we establish results on so-called minimal cover classes with respect to the introduced majorization.

KW - Doubly stochastic matrix

KW - Matrix majorization

KW - Partial order

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Majorization for matrix classes

Abstract

Bibliographical note

Funding

Keywords

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