Cavers, Michael S, In-Jae Kim, Bryan L. Shader, and Kevin N. Vander Meulen. “On determining minimal spectrally arbitrary patterns.” Electronic Journal of Linear Algebra 13 (2005): 240–248.
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.