Spectrally arbitrary pattern extensions

A matrix pattern is often either a sign pattern with entries in {0,+,−} or, more simply, a nonzero pattern with entries in {0,⁎}. A matrix pattern A is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix having the pattern A and the chosen spectrum. We describe a graphical technique, a triangle extension, for constructing spectrally arbitrary patterns out of some known lower order spectrally arbitrary …