On the ellipticity of the higher rank numerical range

2025/12/02 by Bebiano, Natália, Lemos, Rute, Soares, Graça
#15A60 #47A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.02977

Abstract

The higher rank numerical range is a concept that generalizes the classical numerical range, and it has application in quantum error correction. We investigate these sets for 2-by-2 block matrices with associated Kippenhahn curves consisting of ellipses (and eventually points). As a consequence, elliptical higher rank numerical range results are derived in a unified way, using an approach developed by Spitkovsky \it et al.

Citations

• The convex algebraic geometry of higher-rank numerical ranges
• Unified approach to reciprocal matrices with Kippenhahn curves containing elliptical components
• On Kippenhahn curves and higher-rank numerical ranges of some matrices
• Kippenhahn curves of some tridiagonal matrices
• On the numerical range of some block matrices with scalar diagonal blocks
• On the higher rank numerical range of the shift operator

Related

• The convex algebraic geometry of higher-rank numerical ranges
• Elementary constructive approach to the higher-rank numerical ranges of unitary matrices
• On Kippenhahn curves and higher-rank numerical ranges of some matrices
• Low-dimensional reciprocal matrices with elliptical components of their Kippenhahn curves
• Higher Rank Numerical Ranges of Jordan-Like Matrices