Abstract :
It was shown by R. E. Hartwig and M. S. Putcha and independently by P. Y. Wu that the complex square matrix T is a sum of finitely many idempotent matrices if and only if tr T is an integer and tr T ≥ rank T. We determine the minimal number of required idempotents for such matrices in terms of their traces and sizes, and we completely solve the problem for matrices T with size 2, 3, 4, or 5, also, we give some sufficient/necessary conditions for a complex matrix T to be the sum of three or more idempotents.
