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arXiv · 1712.00744

The quaternionic Gauss-Lucas Theorem

Riccardo Ghiloni·Alessandro Perotti
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Abstract

The classic Gauss-Lucas Theorem for complex polynomials of degree $d\ge2$ has a natural reformulation over quaternions, obtained via rotation around the real axis. We prove that such a reformulation is true only for $d=2$. We present a new quaternionic version of the Gauss-Lucas Theorem valid for all $d\geq2$, together with some consequences.

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Riccardo Ghiloni, Alessandro Perotti. 2017-12-03. The quaternionic Gauss-Lucas Theorem. https://doi.org/10.1007/s10231-018-0742-z

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