Idempotency of linear combinations of commuting three tripotent matrices

Abstract

Given nonzero commuting tripotent matrices T1,T2 and 3 T , i.e., 3 = i i T T and TiTj =TjTi, i, j = 1, 2, 3, the problem of characterizing all situations, in which a linear combination1 1 2 2 3 3 A = c T + c T + c T where 1 2 3 c ,c ,c ?????? \{0}is an idempotent matrix, is studied.