On a disjoint idempotent decomposition for linear combinations produced from n commutative tripotent matrices

It has been established a 3n3n-term disjoint idempotent decomposition (DID) for the linear combinations produced from n  (⩾2)(⩾2) commutative tripotent matrices, their products and their products of power 2 at most. The results obtained in this way generalize those in [Y. Tian, A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications, Linear Multilinear Algebra 59 (2011) 1237–1246]. Moreover, an algorithm to get a DID has been provided. Finally, a numerical example has been given to exemplify the results.