Maps preserving zeros of matrix polynomials

A. Guterman; B. Kuzma

doi:10.1134/s1064562409040152

Maps preserving zeros of matrix polynomials

A. Guterman, B. Kuzma

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

2 Scopus citations

Abstract

We study non-linear maps on the set of n × n matrices over a field, which preserve the zeros of a fixed homogeneous multilinear polynomial. This solves Kaplansky-Watkins problem from 1976 about the structure of such transformations.

Original language	English
Pages (from-to)	508-510
Number of pages	3
Journal	Doklady Mathematics
Volume	80
Issue number	1
DOIs	https://doi.org/10.1134/s1064562409040152
State	Published - Aug 2009
Externally published	Yes

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS This work was partially supported by the Russian-Slovenian cooperation grant BI-RV/08-09-009. A. Guterman also acknowledges the support of the Russian Foundation for Basic Research, project no. 08-01-00693a.

Funding

ACKNOWLEDGMENTS This work was partially supported by the Russian-Slovenian cooperation grant BI-RV/08-09-009. A. Guterman also acknowledges the support of the Russian Foundation for Basic Research, project no. 08-01-00693a.

Funders	Funder number
Russian Foundation for Basic Research	08-01-00693a

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10.1134/s1064562409040152

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title = "Maps preserving zeros of matrix polynomials",

abstract = "We study non-linear maps on the set of n × n matrices over a field, which preserve the zeros of a fixed homogeneous multilinear polynomial. This solves Kaplansky-Watkins problem from 1976 about the structure of such transformations.",

author = "A. Guterman and B. Kuzma",

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Maps preserving zeros of matrix polynomials

Abstract

Bibliographical note

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