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Orbit closure hierarchies of skew-symmetric matrix pencils. (English) Zbl 1315.15012

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 \(C-\lambda D\).

MSC:

15A22 Matrix pencils
15A21 Canonical forms, reductions, classification
15B57 Hermitian, skew-Hermitian, and related matrices

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