Spectral inclusion sets for structured matrices

Abstract

We derive eigenvalue inclusion sets for centrohermitian, skew-centrohermitian, perhermitian, skew-perhermitian, and persymmetric matrices, that can be considered structured analogs of the Geršgorin sets. We also present nonsingularity conditions associated with these spectral inclusion sets. In addition, we derive sets that can be considered the structured analogs of the Brauer sets. Our techniques are general enough to allow for other symmetries as well.