A Class of Spectrally Arbitrary Ray Patterns

Abstract

An $n×n$ ray pattern $A$ is said to be spectrally arbitrary if for every monic $n$th degree polynomial $f(x)$ with coefficients from $\mathbb{C},$ there is a complex matrix in the ray pattern class of $A$ such that its characteristic polynomial is $f(x).$ In this paper, a family ray patterns is proved to be spectrally arbitrary by using Nilpotent-Jacobian method.