Mathematical Physics
arXiv:2512.10872 (math-ph)
[Submitted on 11 Dec 2025 (v1), last revised 24 Jun 2026 (this version, v3)]
Abstract:We revisit the classical problem of alignment in products of positive matrices. A direct analysis yields a sharp product misalignment bound, providing an elementary route to alignment and Birkhoff's contraction formula.
| Comments: | 8 pages; revised exposition and simplified proofs; main results unchanged; equivalence with classical results added |
| Subjects: | Mathematical Physics (math-ph); Dynamical Systems (math.DS); Functional Analysis (math.FA) |
| Cite as: | arXiv:2512.10872 [math-ph] |
| (or arXiv:2512.10872v3 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2512.10872 arXiv-issued DOI via DataCite |
Submission history
From: Evgenij Kritchevski [view email]
[v1]
Thu, 11 Dec 2025 18:03:11 UTC (24 KB)
[v2]
Tue, 30 Dec 2025 00:54:03 UTC (22 KB)
[v3]
Wed, 24 Jun 2026 20:28:42 UTC (6 KB)
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