On semimonotone matrices of exact order two
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912934353960960 |
|---|---|
| author | Chauhan, Bharat Pratap Dubey, Dipti |
| author_facet | Chauhan, Bharat Pratap Dubey, Dipti |
| contents | In this paper, we introduce the notion of (strictly) semimonotone matrices of exact order $k$, where $0\leq k\leq n$, and explore their properties. We fully characterize the $3 \times 3$ (strictly) semimonotone matrices of exact order $2$, and show that the class of $3 \times 3$ semimonotone matrices of exact order $2$ forms a subclass of inverse $\mathbf{Z}$-matrices. We further investigate $ n\times n$ (strictly) semimonotone matrices of exact order $2$, with emphasis on their identification and construction, and establish that every $n\times n$ semimonotone $\mathbf{Z}$-matrix of exact order $2$ is invertible. Additionally, we show that when $n-k=1$, the class of (strictly) semimonotone matrices of exact order $k$ is a subclass of $\mathbf{Z}$-matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00639 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On semimonotone matrices of exact order two Chauhan, Bharat Pratap Dubey, Dipti Optimization and Control 15A15, 15A18, 15B48 In this paper, we introduce the notion of (strictly) semimonotone matrices of exact order $k$, where $0\leq k\leq n$, and explore their properties. We fully characterize the $3 \times 3$ (strictly) semimonotone matrices of exact order $2$, and show that the class of $3 \times 3$ semimonotone matrices of exact order $2$ forms a subclass of inverse $\mathbf{Z}$-matrices. We further investigate $ n\times n$ (strictly) semimonotone matrices of exact order $2$, with emphasis on their identification and construction, and establish that every $n\times n$ semimonotone $\mathbf{Z}$-matrix of exact order $2$ is invertible. Additionally, we show that when $n-k=1$, the class of (strictly) semimonotone matrices of exact order $k$ is a subclass of $\mathbf{Z}$-matrices. |
| title | On semimonotone matrices of exact order two |
| topic | Optimization and Control 15A15, 15A18, 15B48 |
| url | https://arxiv.org/abs/2603.00639 |