Decomposition of matrices into a sum of invertible matrices and matrices of fixed index
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914726698549248 |
|---|---|
| author | Danchev, Peter García, Esther Lozano, Miguel Gómez |
| author_facet | Danchev, Peter García, Esther Lozano, Miguel Gómez |
| contents | 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 $\mathbb{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12751 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposition of matrices into a sum of invertible matrices and matrices of fixed index Danchev, Peter García, Esther Lozano, Miguel Gómez Rings and Algebras 15A21, 15A24, 15B99, 16U60 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 $\mathbb{F}$. |
| title | Decomposition of matrices into a sum of invertible matrices and matrices of fixed index |
| topic | Rings and Algebras 15A21, 15A24, 15B99, 16U60 |
| url | https://arxiv.org/abs/2302.12751 |