Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices

Hong You,Xiao Min Tang

doi:10.1016/j.laa.2003.10.008

Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices

Hong You, Xiao Min Tang

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https://doi.org/10.1016/j.laa.2003.10.008

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Journal: Linear Algebra and Its Applications	Publication Date: Mar 1, 2004
Citations: 14	License type: publisher-specific-oa

Affiliation: Harbin Institute of Technology, Heilongjiang University

#Symmetric Matrices #Alternate Matrices + Show 2 more

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Abstract

Denote the set of n× n symmetric matrices (resp. alternate matrices) over a field F by S n( F ) (resp. K n( F ) ). We characterize the bijective additive preservers of rank-additivity on S n( F ) and K n( F ) . The set S n( F ) (resp. K n( F ) ) forms a non-associative ring with respect to the addition ( A, B)↦ A+ B and the multiplication ( A, B)↦ A· B= ABA where A,B∈S n( F ) (resp. K n( F ) ). The forms of any automorphism of the two non-associative rings are also given.

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