2019/03/24 by Monimala Nej, Nej, Monimala, A. Satyanarayana Reddy +1
Computer Science · Engineering · Physics and Astronomy · #05C38 #05C50 #15B99 #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1903.09963
openalex publication_date 2019/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A nonnegative matrix A is said to be \it primitive if for some positive integer m, entries in Am are positive, notationally represented as Am>0. The smallest such m is called the \it exponent of A, denoted exp(A). For the class of primitive companion matrices X, we find exp(A) for certain A ∈ X. Thereafter, we find certain numbers in En(X), where En(X)=\m ∈ \N : there exists an n × n matrix A in X with exp(A)=m\. At the end we propose open problems for further research.