Speaker
Jephian C.-H. Lin
(National Yang Ming Chiao Tung University)
Description
A sign pattern is a matrix whose entries are in $\{+, -, 0\}$, while its quantitative class is the set of real matrices whose entries match the corresponding signs. A sign pattern is said to be spectrally arbitrary if its quantitative class contains matrices demonstrating all possible monic real polynomials as the characteristic polynomials. Historically, there are the Jacobian method, the nilpotent-centralizer method, and the nonsymmetric strong spectral property (SSP, which is equivalent to the similarity-transversality property) to witness a spectrally arbitrary sign pattern. However, their relations are unclear. In this talk, we survey these methods and show that they are equivalent when the minimal polynomial has degree $n$.
Authors
Prof.
Minerva Catral
(Xavier University)
Shaun Fallat
(University of Regina)
Dr
Himanshu Gupta
(University of Regina)
Jephian C.-H. Lin
(National Yang Ming Chiao Tung University)