Some additive decompositions of $\mathbb{K}$-regular matrices

TL;DR

This paper investigates conditions under which certain additive decompositions of $\\mathbb{K}$-regular matrices exist, are unique, and possess specific properties, using convergent series under particular hypotheses.

Contribution

It introduces new criteria for additive decompositions of $\\mathbb{K}$-regular matrices and analyzes their uniqueness and properties under specific conditions.

Findings

Established existence criteria for additive decompositions.

Proved uniqueness of the decompositions under certain hypotheses.

Analyzed properties of the decompositions and their images through convergent series.

Abstract

Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.