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arXiv · 1712.03393

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

Peter Loly·Ian Cameron·Adam Rogers
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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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Peter Loly, Ian Cameron, Adam Rogers. 2017-12-09. Powers of doubly-affine integer square matrices with one non-zero eigenvalue. https://arxiv.org/abs/1712.03393

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