A rank equality for the sum of finitely many tripotent matrices

In the first chapter, it is presented some brief literature information related to the matrices idempotent, involutive and tripotent and also pointed out the importance of the concept of the rank. Some fundamental concepts and properties which will be used throughout the study, are given in the second chapter. A relation between the rank of the sum of the nxn complex matrices M and the sum of the ranks of these matrices is established in the third chapter. In the fourth chapter, it is handled a problem which is similar to the problem in the third chapter for the family of tripotent matrices which covers the family of the involutive matrices. It is also noted that the main result obtained in this chapter covers many results that exist in the literature for the family of idempotent matrices.