A generalization of Rohn's theorem on full-rank interval matrices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866929608994062336 |
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| author | Rubei, Elena |
| author_facet | Rubei, Elena |
| contents | A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of the set of the real numbers, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in the set of real numbers. We say that a matrix $A$ with constant entries is contained in a general closed interval matrix $μ$ if and only if, for every $i,j$, we have that $A_{i,j} \in μ_{i,j}$. Rhon characterized full-rank square interval matrices, that is, square interval matrices $μ$ such that every constant matrix contained in $μ$ is nonsingular. In this paper we generalize this result to general closed interval matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_05433 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A generalization of Rohn's theorem on full-rank interval matrices Rubei, Elena Rings and Algebras 15A99, 15A03 A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of the set of the real numbers, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in the set of real numbers. We say that a matrix $A$ with constant entries is contained in a general closed interval matrix $μ$ if and only if, for every $i,j$, we have that $A_{i,j} \in μ_{i,j}$. Rhon characterized full-rank square interval matrices, that is, square interval matrices $μ$ such that every constant matrix contained in $μ$ is nonsingular. In this paper we generalize this result to general closed interval matrices. |
| title | A generalization of Rohn's theorem on full-rank interval matrices |
| topic | Rings and Algebras 15A99, 15A03 |
| url | https://arxiv.org/abs/1803.05433 |