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Powers of doubly-affine integer square matrices with one non-zero eigenvalue

2017/12/09 by Peter Loly, Ian Cameron, Loly, Peter +3
Mathematics · #15 #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO) #math.CO #math.HO #msc:15

paper · pdf · doi:10.48550/arxiv.1712.03393

24 pages, 10 tables

arxiv created 2017/12/09 · arxiv updated 2017/12/12

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.

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