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Higher Derivations and the Jordan Canonical Form of the Companion Matrix

Published online by Cambridge University Press:  20 November 2018

Leslie G. Roberts
Leslie G. Roberts*
Affiliation:
Queen's University, Kingston, Ontario
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The purpose of this note is to give a basis with respect to which the companion matrix of an equation (over a field of any characteristic) is in Jordan canonical form.

Let k be a field. Define a k-linear map Di:k[X]→k[X] by where the integer is the binomial coefficient n!;/i!;(n —i)!;. We adopt the usual convention that if i>9 or j<0. Then D=(D0, D1D2,…) is a higher derivation (see [1, p. 192]).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 143 - 144
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Jacobson, N., Lectures in abstract algebra, Vol. 3, Theory of fields and Galois theory. Van Nostrand, Princeton, N.J., 1964.Google Scholar