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A lower bound for the degree of polynomials satisfied by matrices

Part of: Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

K. R. Pearson
K. R. Pearson
Affiliation:
La Trobe UniversityBundoora, Victoria, 3083 Australia
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Abstract

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R. Paré and W. Schelter (1978) have extended the Cayley-Hamilton theorem by showing that for each n<1 there is an integer k such that all n x n matrices over any (possibly noncommutative) ring satisfy a monic polynomial of degree k. We give a lower bound for this degree, namely π(n), which is defined as the shortest possible length of a sequence with entries from {1, 2, …, n}.

Keywords

matrixnoncommutative ringpolynomialCayley-Hamilton theorem

MSC classification

Secondary: 15A24: Matrix equations and identities
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 430 - 436
Copyright
Copyright © Australian Mathematical Society 1979

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