Sums Of K-potent Matrices

Abstract

We study sums of k-potent matrices. We show the conditions by which a complex matrix A can be expressed as a sums of k-potent matrices. Also we obtain conditions by which a complex matrix A can be expressed as a sum of finite order elements. This generalize some results obtain by Wu in [2]. Also we study the sum of k-potent matrices in M Cf (F ) with F be a field and proof that any matrix in this space can be expressed as a sum of 14 (k + 1)-potent matrices preserving the result obtain by Slowik in [3].