# Higher Rank Numerical Ranges of Jordan-Like Matrices

## TL;DR

This paper fully characterizes the higher rank numerical ranges of Jordan-like matrices, providing insights into their extreme properties and offering concrete examples.

## Contribution

It offers a complete characterization of higher rank numerical ranges for matrices combining Jordan blocks and scalar multiples of the identity, a novel theoretical result.

## Key findings

- Complete characterization of higher rank numerical ranges for Jordan-like matrices
- Identification of extreme properties of these numerical ranges
- Provision of concrete examples illustrating these properties

## Abstract

We completely characterize the higher rank numerical range of the matrices of the form $J_n(\alpha)\oplus\beta I_m$, where $J_n(\alpha)$ is the $n\times n$ Jordan block with eigenvalue $\alpha$. Our characterization allows us to obtain concrete examples of several extreme properties of higher rank numerical ranges.