Mathematics > Classical Analysis and ODEs
arXiv:2307.13142 (math)
[Submitted on 24 Jul 2023 (v1), last revised 4 Aug 2026 (this version, v3)]
Abstract:For the class of $d\times d$ matrices $B=[b_{i,j}]$ with complex nonzero entries satisfying $\sum_{i=1}^{d}|b_{i,j}|=1$, we provide the conditions for the convergence of power matrices $B^n$ to a nonzero limit matrix.
| Comments: | 5 pages, a revised version after addressing referee's comments |
| Subjects: | Classical Analysis and ODEs (math.CA); Complex Variables (math.CV); Probability (math.PR) |
| MSC classes: | Primary 30A99, Secondary 15A16, 15B51 |
| Cite as: | arXiv:2307.13142 [math.CA] |
| (or arXiv:2307.13142v3 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2307.13142 arXiv-issued DOI via DataCite |
Submission history
From: Vyacheslav M. Abramov [view email]
[v1]
Mon, 24 Jul 2023 21:50:34 UTC (7 KB)
[v2]
Mon, 25 Sep 2023 04:17:42 UTC (8 KB)
[v3]
Tue, 4 Aug 2026 03:01:58 UTC (7 KB)
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