Bundles of skew-symmetric matrix pencils and their minimal degenerations

Journal article, 2026

Small perturbations to the coefficients of a skew-symmetric matrix pencil can cause large changes in its complete eigenstructure, e.g., eigenvalues, their multiplicities, as well as minimal indices may change. In this manuscript, we state three results: (a) the characterization of inclusion between the closures of congruence bundles of skew-symmetric matrix pencils; (b) the necessary and sufficient condition for one congruence bundle of a skew-symmetric matrix pencil, P, to belong to the closure of the congruence bundle of another matrix pencil, Q, such that there is no matrix pencil, R, whose bundle contains the closure of the bundle of P and is contained in the closure of the bundle of Q; and (c) bundles are open in their closures.