The classic Gauss-Lucas theorem for complex polynomials of degree $dge2$ 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 $dgeq2$, together with some consequences.
The quaternionic Gauss-Lucas theorem / Ghiloni, Riccardo; Perotti, Alessandro. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - STAMPA. - 197:6(2018), pp. 1679-1686. [10.1007/s10231-018-0742-z]
The quaternionic Gauss-Lucas theorem
Riccardo Ghiloni;Alessandro Perotti
2018-01-01
Abstract
The classic Gauss-Lucas theorem for complex polynomials of degree $dge2$ 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 $dgeq2$, together with some consequences.File in questo prodotto:
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