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On Matrix Commutators of Higher Order

Published online by Cambridge University Press:  20 November 2018

D. W. Robinson
D. W. Robinson*
Affiliation:
Brigham Young University
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Let Fn be the collection of n-by-n matrices over a field F. For Y in Fn let ΔY be the mapping on Fn given by XΔY = XY — YX. In this paper we study the following

Proposition. Let A and B be in Fn and let m be a positive integer. If BΔxm = 0 whenever XΔAm = 0, then B is a polynomial in A with coefficients in F.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 527 - 532
Copyright
Copyright © Canadian Mathematical Society 1965

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