Minimal degenerations of orbits of skew-symmetric matrix pencils
Abstract
The complete eigenstructure, i.e. eigenvalues with multiplicities and minimal indices, of a skew-symmetric matrix pencil may change drastically if the matrix coefficients of the pencil are subjected to (even small) perturbations. These changes can be investigated qualitatively by constructing the stratification (closure hierarchy) graphs of the congruence orbits of the pencils. The results of this paper facilitate the construction of such graphs by providing all closest neighbours for a given node in the graph. More precisely, we prove a necessary and sufficient condition for one congruence orbit of a skew-symmetric matrix pencil, A, to belong to the closure of the congruence orbit of another pencil, B, such that there is no pencil, C, whose orbit contains the closure of the orbit of A and is contained in the closure of the orbit of B.
Fields of Study & Subjects
Matrix Theory and Algorithms
Quasicrystal Structures and Properties
Holomorphic and Operator Theory
Publication details
- Journal / source
- Linear and Multilinear Algebra
- Publisher
- Informa UK Limited
- Volume
- 74
- Issue
- 3
- Pages
- 255–275
- Publication date
- 26 January 2026
- Language
- EN