Article
| Title: | Minimal completion of $I\times J$ doubly substochastic matrices (English) |
| Author: | Dadkhah, Mohammad |
| Author: | Bayati Eshkaftaki, Ali |
| Author: | Manjegani, Seyed Mahmoud |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 3 |
| Year: | 2025 |
| Pages: | 853-864 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | For a given $I\times J$ doubly substochastic matrix $A$, by adding a (cardinal) number of columns or rows, we want to obtain a doubly stochastic matrix $D$ that contains $A$ as a sub-matrix. Then it is shown that there are minimal (cardinal) numbers of such cardinal numbers, which we call row sub-defect and column sub-defect of $A$. We also try to obtain these two values in some cases. (English) |
| Keyword: | doubly (sub)stochastic |
| Keyword: | minimal completion |
| Keyword: | semi-infinite |
| Keyword: | row sub-defect |
| Keyword: | column sub-defect |
| MSC: | 15A03 |
| MSC: | 15A04 |
| MSC: | 15A83 |
| MSC: | 47L05 |
| DOI: | 10.21136/CMJ.2025.0450-24 |
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| Date available: | 2025-09-19T11:53:32Z |
| Last updated: | 2025-09-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153056 |
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| Reference: | [5] Eshkaftaki, A. Bayati: Minimal completion of $I \times I$ doubly substochastic matrices.Linear Multilinear Algebra 70 (2022), 2065-2077. Zbl 07559560, MR 4452526, 10.1080/03081087.2020.1781754 |
| Reference: | [6] Eshkaftaki, A. Bayati: Sub-defect of product of $I\times I$ finite sub-defect matrices.Linear Multilinear Algebra 72 (2024), 1581-1589. Zbl 1546.15022, MR 4766047, 10.1080/03081087.2023.2188157 |
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| Reference: | [11] Ljubenović, M., Djordjević, D. S.: Linear preservers of weak majorization on $\ell^1(I)^+$ when $I$ is an infinite set.Linear Algebra Appl. 517 (2017), 177-198. Zbl 1387.47023, MR 3592018, 10.1016/j.laa.2016.12.012 |
| Reference: | [12] Manjegani, S. M., Moein, S.: Majorization and semidoubly stochastic operators on $L^{1}(X)$.J. Inequal. Appl. 2023 (2023), Article ID 27, 20 pages. Zbl 07772804, MR 4552121, 10.1186/s13660-023-02935-z |
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