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

2019/07/31 by Luís Carvalho, Carvalho, Luís, Cristina Diogo +3 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Graph theory and applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1907.13438

openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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