Powers of doubly-affine integer square matrices with one non-zero eigenvalue
History and Overview
2017-12-12 v1 Combinatorics
Abstract
When doubly-affine matrices such as Latin and magic squares with a single non-zero eigenvalue are powered up they become constant matrices after a few steps. The process of compounding squares of orders m and n can then be used to generate an infinite series of such squares of orders mn. The Cayley-Hamilton theorem is used to understand this property, where their characteristic polynomials have just two terms.
Cite
@article{arxiv.1712.03393,
title = {Powers of doubly-affine integer square matrices with one non-zero eigenvalue},
author = {Peter Loly and Ian Cameron and Adam Rogers},
journal= {arXiv preprint arXiv:1712.03393},
year = {2017}
}
Comments
24 pages, 10 tables