Low-dimensional reciprocal matrices with elliptical components of their Kippenhahn curves

2021/05/26 by Jiang, Muyan, Spitkovsky, Ilya M.
#15A60 #47B36 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.12664

Abstract

By definition, reciprocal matrices are tridiagonal n-by-n matrices A with constant main diagonal and such that a_i,i+1a_i+1,i=1 for i=1,…,n-1. For n≤ 6, we establish criteria under which the numerical range generating curves (also called Kippenhahn curves) of such matrices consist of elliptical components only. As a corollary, we also provide a complete description of higher-rank numerical ranges when the criteria are met.

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