The uniform normal form of a linear mapping

preprint2014arXivOpen access

Abstract

Let VV be a finite dimensional vector space over a field k\mathrm{k} of characteristic 00. Let AA be a linear mapping of VV into itself. This paper gives a normal form for AA, which gives a better description of the structure of AA than the companion matrix. The computation of this normal form uses only operations from k\mathrm{k} and does not require finding roots of any polynomial.

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