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. Also we study the sum of $k$-potent matrices in ${\mathcal{M}}_{\mathcal{C}f}(F)$ 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.

References in corpus (1)

• Expressing Finite-Infinite Matrices Into Products of Commutators of Finite Order Elements

Cited by in corpus (1)

• $(k+1)$-potent Matrices in triangular matrix Groups and Incidence Algebras of Finite Posets