A general linear random-effects model that includes both fixed and random effects, and its two subsample models are considered without making any restrictions on correlation of random effects and any full rank assumptions. ...
Let T-1 and T-2 be two nonzero commuting n x n tripotent matrices and c(1), c(2) two nonzero complex numbers. Necessary and sufficient conditions for the tripotency and the idempotency of c(1)T(1) + c(2)T(2) are obtained. ...