Kippenhahn curves of some tridiagonal matrices
Nat\'alia Bebiano, Jo\'ao da Provid\'encia, Ilya M. Spitkovsky, Kenya, Vazquez
TL;DR
This paper investigates the geometric properties of certain tridiagonal matrices, specifically identifying conditions under which their numerical ranges form ellipses, with a focus on small matrix sizes up to 6-by-6.
Contribution
It provides new criteria for when these specific tridiagonal matrices have elliptical numerical ranges, expanding understanding of their spectral geometry.
Findings
Conditions for 2x2 to 6x6 matrices to have elliptical numerical ranges
Characterization of matrices with reciprocal off-diagonal entries
Extension of numerical range analysis to small-sized matrices
Abstract
Tridiagonal matrices with constant main diagonal and reciprocal pairs of off-diagonal entries are considered. Conditions for such matrices with sizes up to 6-by-6 to have elliptical numerical ranges are obtained.
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