k-Potence preserving maps without the linearity and surjectivity assumptions |
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Authors: | Hong You |
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Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China |
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Abstract: | Let Mn be the space of all n × n complex matrices, and let Γn be the subset of Mn consisting of all n × n k-potent matrices. We denote by Ψn the set of all maps on Mn satisfying A − λB ∈ Γn if and only if ?(A) − λ?(B) ∈ Γn for every A,B ∈ Mn and λ ∈ C. It was shown that ? ∈ Ψn if and only if there exist an invertible matrix P ∈ Mn and c ∈ C with ck−1 = 1 such that either ?(A) = cPAP−1 for every A ∈ Mn, or ?(A) = cPATP−1 for every A ∈ Mn. |
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Keywords: | 15A04 |
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