Permanent Polya problem for additive surjective maps

A. E. Guterman, I. A. Spiridonov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Let Mn(F) denote the set of square matrices of size n over a field F with characteristics different from two. We say that the map f:Mn(F)→Mn(F) is additive if f(A+B)=f(A)+f(B) for all A,B∈Mn(F). The main goal of this paper is to prove that for n>2 there are no additive surjective maps T:Mn(F)→Mn(F) such that per(T(A))=det⁡(A) for all A∈Mn(F). Also we show that an arbitrary additive surjective map T:Mn(F)→Mn(F) which preserves permanent is linear and thus can be completely characterized.

Original languageEnglish
Pages (from-to)140-155
Number of pages16
JournalLinear Algebra and Its Applications
StatePublished - 15 Aug 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.


This work was financially supported by the Russian Science Foundation under grant 16-11-10075 .

FundersFunder number
Russian Science Foundation16-11-10075


    • Additive maps
    • Determinant
    • Linear maps
    • Permanent


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