Weakly commuting maps on the set of rank-1 matrices

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Weakly commuting maps on the set of rank-1 matrices

Franca, Willian

Linear & multilinear algebra, 03/2017, Volume: 65, Issue: 3

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Let be a natural number. Let be the ring of all matrices over an arbitrary field . In the present paper, we will find the description of all additive mappings such that for all , where ( and are matrices units). As an application we will characterize all additive maps such that for all , where represents the set formed by all rank-1 matrices of . Precisely, we will show that for all if and only if for all .

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