On determining minimal spectrally arbitrary patterns

Abstract

A new family of minimal spectrally arbitrary patterns is presented which allow for
arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson,
D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121-
137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding
an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.