The decomposition of idempotents associated with inflators (Q1097935)

This paper deals with a new class of matrices called inflators, which was recently introduced by \textit{S. Friedland}, \textit{D. Hershkowitz} and \textit{H. Schneider} [Trans. Am. Math. Soc. 300, 343-366 (1987; Zbl 0619.15018)]. It is shown that the idempotent matrix (with rank greater than one) associated with an inflator can be decomposed into several pairwise orthogonal idempotents of lower rank such that the resultant idempotents are associated with inflators which are inflation product factors of the original inflator. The resultant idempotents from a decomposition are not generally unique and their total number is exactly the rank of the original idempotent. An illustrative example is given.