Several spectrally arbitrary ray patterns

A ray pattern A of order n is said to be spectrally arbitrary if given any monic nth degree polynomial f(x) with coefficients from ℂ, there exists a matrix realization of A such that its characteristic polynomial is f(x). An n × n ray pattern A is said to be minimally spectrally arbitrary if replacing any nonzero entry of A by zero destroys this property. In this article, several families of ray patterns are presented and proved to be minimally spectrally arbitrary. We also show that for n ≥ 5, when A n is spectrally arbitrary, then it is minimally spectrally arbitrary.