Linear converters of weak, directional and strong majorizations

Alexander Guterman, Pavel Shteyner

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In the theory of matrix majorizations there are three types of majorizations that play an important role. These are weak, strong and directional majorizations for matrices. In this paper we characterize the linear operators converting each one of these majorizations to another one.

Original languageEnglish
Pages (from-to)320-346
Number of pages27
JournalLinear Algebra and Its Applications
StatePublished - 15 Mar 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.


A characterization of linear converters from directional to strong majorization ( Theorem 4.5 ) was supported by the Russian Federation Government (Grant number 075-15-2019-1926 ). The characterization of converters from weak majorization ( Theorem 5.4 ) was supported by the Ministry of Science and Higher Education of the Russian Federation (Goszadaniye No. 075-00337-20-03, project No. 0714-2020-0005 ).

FundersFunder number
Government Council on Grants, Russian Federation075-15-2019-1926
Ministry of Science and Higher Education of the Russian Federation0714-2020-0005, 075-00337-20-03


    • Linear converters
    • Linear preservers
    • Matrix majorization
    • Vector majorization


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