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2020 Structured sequences and matrix ranks
Charles Johnson, Yaoxian Qu, Duo Wang, John Wilkes
Involve 13(1): 1-8 (2020). DOI: 10.2140/involve.2020.13.1

Abstract

We consider infinite sequences from a field and all matrices whose rows consist of distinct consecutive subsequences. We show that these matrices have bounded rank if and only if the sequence is a homogeneous linear recurrence; moreover, it is a k -term linear recurrence if and only if the maximum rank is k . This means, in particular, that the ranks of matrices from the sequence of primes are unbounded. Though not all matrices from the primes have full rank, because of the Green–Tao theorem, we conjecture that square matrices whose entries are a consecutive sequence of primes do have full rank.

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Charles Johnson. Yaoxian Qu. Duo Wang. John Wilkes. "Structured sequences and matrix ranks." Involve 13 (1) 1 - 8, 2020. https://doi.org/10.2140/involve.2020.13.1

Information

Received: 9 May 2016; Revised: 13 September 2016; Accepted: 9 April 2017; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07172108
MathSciNet: MR4059938
Digital Object Identifier: 10.2140/involve.2020.13.1

Subjects:
Primary: 15A03
Secondary: 11B25, 11B37

Rights: Copyright © 2020 Mathematical Sciences Publishers

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