Title: On the Gauss-Lucas theorem in the quaternionic setting
Abstract: In theory of one complex variable, Gauss-Lucas Theorem states that the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the polynomial. The exact analogue of this result cannot hold, in general, in the quaternionic case; instead, the critical points of a non constant polynomial belong to the convex hull of the set of zeros of the so-called symmetrization of the given polynomial. An incomplete proof of this statement was given in [8]. In this paper we present a different but complete proof of this theorem and we discuss a consequence.
Publication Year: 2017
Publication Date: 2017-11-06
Language: en
Type: preprint
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Cited By Count: 1
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