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arXiv · 2302.12751

Decomposition of matrices into a sum of invertible matrices and matrices of fixed index

Peter Danchev·Esther García·Miguel Gómez Lozano
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Abstract

For any $n\ge 2$ and fixed $k\ge 1$, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k=0$ over an arbitrary field $\mathbb{F}$.

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Peter Danchev, Esther García, Miguel Gómez Lozano. 2023-02-24. Decomposition of matrices into a sum of invertible matrices and matrices of fixed index. https://doi.org/10.13001/ela.2023.7851

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