Rocky Mountain Journal of Mathematics

Exponents of primitive companion matrices

Monimala Nej and A. Satyanarayana Reddy

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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.

Article information

Rocky Mountain J. Math., Volume 49, Number 5 (2019), 1633-1645.

First available in Project Euclid: 19 September 2019

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Zentralblatt MATH identifier

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Secondary: 05C38: Paths and cycles [See also 90B10] 15B99: None of the above, but in this section

primitive matrix companion matrix exponent


Nej, Monimala; Reddy, A. Satyanarayana. Exponents of primitive companion matrices. Rocky Mountain J. Math. 49 (2019), no. 5, 1633--1645. doi:10.1216/RMJ-2019-49-5-1633.

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