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2019 Exponents of primitive companion matrices
Monimala Nej, A. Satyanarayana Reddy
Rocky Mountain J. Math. 49(5): 1633-1645 (2019). DOI: 10.1216/RMJ-2019-49-5-1633

Abstract

A nonnegative matrix $A$ is primitive if for some positive integer $m$ all entries in $A^m$ are positive. The smallest such $m$ is called the exponent of $A$ and written $\exp (A)$. For the class of primitive companion matrices $X$, we find $\exp (A)$ for certain $A \in X$. We find certain values of $m$ for which there is an $n \times n$ primitive companion matrix (for given $n$) with exponent $m$. We also propose open problems for further research.

Citation

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Monimala Nej. A. Satyanarayana Reddy. "Exponents of primitive companion matrices." Rocky Mountain J. Math. 49 (5) 1633 - 1645, 2019. https://doi.org/10.1216/RMJ-2019-49-5-1633

Information

Published: 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07113702
MathSciNet: MR4010576
Digital Object Identifier: 10.1216/RMJ-2019-49-5-1633

Subjects:
Primary: 05C50
Secondary: 05C38, 15B99

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 5 • 2019
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