A Note on k‐Potence Preservers on Matrix Spaces over Complex Field

Xiaofei Song, Chongguang Cao and Baodong Zheng

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Let ℂ be the field of all complex numbers, Mn the space of all n × n matrices over ℂ, and Sn the subspace of Mn consisting of all symmetric matrices. The map ϕ : Sn → Mn satisfies that A − λB is k‐potent in Sn implying that ϕ(A) − λϕ(B) is k‐potent in Mn, where λ ∈ ℂ, then there exist an invertible matrix P ∈ Mn and ϵ ∈ ℂ with ϵk = ϵ such that ϕ(X) = ϵP−1(X)P for every X ∈ Sn. Moreover, the inductive method used in this paper can be used to characterise similar maps from Mn to Mn.

Date: 2013
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https://doi.org/10.1155/2013/581683

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:581683

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