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arXiv · 2005.00601

Sums Of K-potent Matrices

Ivan Gargate·Michael Gargate
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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.

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Ivan Gargate, Michael Gargate. 2020-05-01. Sums Of K-potent Matrices. https://arxiv.org/abs/2005.00601

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