Matricial Proofs of Some Classical Results about Critical Point Location

被引：1
|
作者：
Johnson, Charles R. [1 ]
Paparella, Pietro [2 ]
机构：
[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[2] Univ Washington, Div Engn & Math, Bothell, WA 98011 USA
来源：
AMERICAN MATHEMATICAL MONTHLY | 2020年 / 127卷 / 01期
关键词：
MSC; VALUES; FIELD;
D O I：
10.1080/00029890.2020.1671740
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Gauss-Lucas and Bocher-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.
引用
收藏
页码：45 / 53
页数：9
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