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2013 A Note on k -Potence Preservers on Matrix Spaces over Complex Field
Xiaofei Song, Chongguang Cao, Baodong Zheng
Abstr. Appl. Anal. 2013(SI20): 1-8 (2013). DOI: 10.1155/2013/581683


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


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Xiaofei Song. Chongguang Cao. Baodong Zheng. "A Note on k -Potence Preservers on Matrix Spaces over Complex Field." Abstr. Appl. Anal. 2013 (SI20) 1 - 8, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1291.15069
MathSciNet: MR3064523
Digital Object Identifier: 10.1155/2013/581683

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI20 • 2013
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