Matrices with invariant by rotation numerical ranges

TL;DR

This paper characterizes matrices whose numerical ranges remain unchanged under rotations by specific angles, revealing symmetry properties related to their structure.

Contribution

It provides a complete characterization of matrices with numerical ranges invariant under rotations of 2π/d, a novel symmetry property.

Findings

Matrices with invariant numerical ranges are characterized by specific structural properties.

The invariance under rotation relates to the eigenvalues and geometric features of the matrices.

The results extend understanding of symmetry in matrix numerical ranges.

Abstract

We characterize the d x d matrices whose numerical ranges are invariant by rotations of angle 2$\pi$/d.