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Prime matrices

Published online by Cambridge University Press:  01 August 2016

P. F. Rivett  and
N. I. P. Mackinnon
P. F. Rivett
Affiliation:
Blundell’s School, Tiverton, Devon EX16 4DN
N. I. P. Mackinnon
Affiliation:
Blundell’s School, Tiverton, Devon EX16 4DN
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Extract

A matrix in a set M of matrices is prime (naturally enough) if it is not the product of any other matrices in the set. We thought we would look for the prime matrices in the set M of all 2 x 2 matrices with entries in the nonnegative integers and with determinant 1. To our great surprise we discovered that:

THEOREM. In M the matrices

are the only primes, and any member of M (except I) can be uniquely factorised into a product of those two.

Type
Research Article
Information
The Mathematical Gazette , Volume 70 , Issue 454 , December 1986 , pp. 257 - 259
Copyright
Copyright © The Mathematical Association 1986

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