摘要

A spectrally arbitrary pattern A is a sign pattern of order n such that every monic real polynomial of degree n can be achieved as the characteristic polynomial of a matrix with sign pattern A. A sign pattern A is minimally spectrally arbitrary if it is spectrally arbitrary but is not spectrally arbitrary if any nonzero entry (or entries) of A is replaced by zero. In this paper, we introduce some new sign patterns which are minimally spectrally arbitrary for all orders n >= 7.