On the convexity and circularity of the numerical range of nilpotent quaternionic matrices

被引：0

作者：

Carvalho, Luis ^{[1
]}

Diogo, Cristina ^{[1
,2
]}

Mendes, Sergio ^{[1
,3
]}

机构：

[1] ISCTE Lisbon Univ Inst, Av das Forcas Armadas, P-1649026 Lisbon, Portugal

[2] Univ Lisbon, Inst Super Tecn, Math Dept, Ctr Math Anal Geometry & Dynam Syst, Av Rovisco Pais, P-1049001 Lisbon, Portugal

[3] Univ Beira Interior, Ctr Matemat & Aplicacoes, Rua Marques DAvila e Bolama, P-6201001 Covilha, Portugal

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2019年 / 25卷

关键词：

quaternions; numerical range; nilpotent matrix;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D + N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range.

引用

页数：20

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