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arXiv · 2012.12708

Matricial Proofs of Some Classical Results about Critical Point Location

Charles R. Johnson·Pietro Paparella
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Abstract

The Gauss--Lucas and B\^{o}cher--Grace--Marden theorems are classical results in the geometry of polynomials. Proofs of the these results are available in the literature, but the approaches are seemingly different. In this work, we show that these theorems can be proven in a unified theoretical framework utilizing matrix analysis (in particular, using the field of values and the differentiator of a matrix). In addition, we provide a useful variant of a well-known result due to Siebeck.

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Charles R. Johnson, Pietro Paparella. 2020-12-21. Matricial Proofs of Some Classical Results about Critical Point Location. https://doi.org/10.1080/00029890.2020.1671740

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