The boundary of the Krein space tracial numerical range, an algebraic approach and a numerical algorithm

Abstract

In this article, tracial numerical ranges associated with matrices in an indefinite inner product space are investigated. The boundary equations of these sets are obtained, and the case of the boundary being a polygon is studied. As an application, a numerical algorithm for plotting the tracial numerical range of an arbitrary complex matrix is presented. Our approach uses the elementary idea that the boundary may be traced by computing the supporting lines.