On maps preserving products equal to fixed elements

We obtain a characterization of bijective linear maps f:Mn(C)→Mn(C) satisfying f(A)f(B)=M whenever AB=N, where M and N are fixed n×n matrices.

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Bibliographic Details
Published in:Journal of algebra 2021-06, Vol.575, p.220-232
Main Authors: Catalano, Louisa, Julius, Hayden
Format: Article
Language:English
Subjects:
Complex matrices
Linear preserver problems
Maps preserving products
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Summary:We obtain a characterization of bijective linear maps f:Mn(C)→Mn(C) satisfying f(A)f(B)=M whenever AB=N, where M and N are fixed n×n matrices.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.02.014