Existence of reciprocal matrices with specified orders for the right and inverse left Perron eigenvectors
Combinatorics
2026-05-19 v1 Optimization and Control
Abstract
Here we give a procedure to construct a reciprocal matrix for which the right and entrywise inverse left Perron eigenvectors have any pair of given orders. An explicit example when the matrix is of size 4 is presented. In particular, it gives an afirmative answer to the question posed in a recent manuscript by Boz\'oki and Csat\'o (2026) about the existence of a reciprocal matrix of size 4 such that the right and entrywise inverse left Perron eigenvectors have reverse orders.
Cite
@article{arxiv.2605.16267,
title = {Existence of reciprocal matrices with specified orders for the right and inverse left Perron eigenvectors},
author = {Susana Furtado and Charles Johnson},
journal= {arXiv preprint arXiv:2605.16267},
year = {2026}
}