On Kippenhahn curves and higher-rank numerical ranges of some matrices

TL;DR

This paper explores the relationship between Kippenhahn curves and higher-rank numerical ranges of matrices, providing detailed analysis for specific classes like tridiagonal 2-periodic matrices.

Contribution

It establishes a connection between Kippenhahn curves and higher-rank numerical ranges, with detailed treatment of tridiagonal 2-periodic matrices.

Findings

Higher-rank numerical ranges can be characterized via Kippenhahn curves.

Explicit descriptions are provided for tridiagonal 2-periodic matrices.

The approach enhances understanding of matrix spectral properties.

Abstract

The higher rank numerical ranges of generic matrices are described in terms of the components of their Kippenhahn curves. Cases of tridiagonal (in particular, reciprocal) 2-periodic matrices are treated in more detail.