Dmytryshyn, Andrii; Kågström, Bo Orbit closure hierarchies of skew-symmetric matrix pencils. (English) Zbl 1315.15012 SIAM J. Matrix Anal. Appl. 35, No. 4, 1429-1443 (2014). The authors study how small perturbations of a skew-symmetric matrix pencil may change its canonical form under congruence. This problem is also known as the stratification problem of skew-symmetric matrix pencil orbits and bundles. That is, they investigate when the closure of the congruence orbit (or bundle) of a skew-symmetric matrix pencil contains the congruence orbit (or bundle) of another skew-symmetric matrix pencil. The developed theory relies on the main theorem stating that a skew-symmetric matrix pencil \(A-\lambda B\) can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil \(C-\lambda D\) if and only if \(A-\lambda B\) can be approximated by pencils congruent to \(C-\lambda D\). Reviewer: Andreas Arvanitoyeorgos (Patras) Cited in 18 Documents MSC: 15A22 Matrix pencils 15A21 Canonical forms, reductions, classification 15B57 Hermitian, skew-Hermitian, and related matrices Keywords:skew-symmetric matrix pencil; stratification; canonical structure information; orbit; bundle Software:StratiGraph PDFBibTeX XMLCite \textit{A. Dmytryshyn} and \textit{B. Kågström}, SIAM J. Matrix Anal. Appl. 35, No. 4, 1429--1443 (2014; Zbl 1315.15012) Full Text: DOI