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On Matrix Commutators of Higher Order
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1965
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