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- W4367000261 abstract "For a matrix $M in K^{n times n}$ we establish a condition on the Galois group of the characteristic polynomial $varphi$ that induces nonvanishing of the minors of the eigenvector matrix of $M$. For $K=mathbb{Z}$ recent results by Eberhard show that, conditionally on the extended Riemann hypothesis, this condition is satisfied with high probability and hence with high probability the minors of eigenvectors matrices of random integer matrices are nonzero. For random graphs this will yield a novel uncertainty principle, related to Chebotarev's theorem on the roots of unity and results from Tao and Meshulam." @default.
- W4367000261 created "2023-04-27" @default.
- W4367000261 creator A5024285661 @default.
- W4367000261 date "2023-04-24" @default.
- W4367000261 modified "2023-10-18" @default.
- W4367000261 title "Chebotarev's nonvanishing minors for eigenvectors of random matrices and graphs" @default.
- W4367000261 doi "https://doi.org/10.48550/arxiv.2304.12075" @default.
- W4367000261 hasPublicationYear "2023" @default.
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