Linear preservers of idempotence on triangular matrix spaces over any field

Abstract

Let F be any field and let T n (F) be the n × n upper triangular matrix space over F. We denote the set of all n × n upper triangular idempotent matrices over F by P n (F).A map ϕ on T n (F) is called a preserver of idempotence if ϕ(P n (F)) ⊂ P n (F); and a strong preserver of idempotence if ϕ(P n (F)) = P n (F).In this paper, we characterize the bijective linear preservers of idempotence on T n (F).Further, the strong linear preservers of idempotence on T n (F) are characterized.

Locations

• International Mathematical Forum - View
• CiteSeer X (The Pennsylvania State University) - View - PDF