An interlacing result for Hermitian matrices in Minkowski space

Abstract

In this paper we will look at the well known interlacing prob-lem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the n ×nma-trix A = Ju−u∗a with a ∈R, J=J∗and u ∈Cn−1. Then Ais H-selfadjoint with respect to the matrix H=In−1⊕(−1). The canonical form for the pair (A, H)plays an important role and the sign characteristic coupled to the pair is also discussed.