Details

Autor(en) / Beteiligte

• Tang, Xiao-Min
• Xu, Jin-Li
• Cao, Chong-Guang

Titel

A note on idempotence-preserving maps

Ist Teil von

• Linear & multilinear algebra, 2008-07, Vol.56 (4), p.399-414

Ort / Verlag

Taylor & Francis Group

Erscheinungsjahr

2008

Quelle

Taylor & Francis

Beschreibungen/Notizen

• Let M n (F) be the space of all n × n matrices over a field F of characteristic not 2, and let P n (F) be the subset of M n (F) consisting of all n × n idempotent matrices. We denote by Φ n (F) the set of all maps from M n (F) to itself satisfying A−λB∈P n (F) implies for every A,B∈M n (F) and λ∈F. In this note, we prove that φ∈Φ n (F) if and only if there exist δ∈{0,1} and an invertible matrix P∈M n (F) such that either for every A∈M n (F), or φ(A)=δPA T P −1 for every A∈M n (F). This improves the result of some related references.