Skip to content
printicon
Show report in:

UMINF 14.02

Orbit closure hierarchies of skew-symmetric matrix pencils

We 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. In other words, we 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. This theory relies on our 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.

Keywords

Skew-symmetric matrix pencil; Stratification; Canonical structure information; Orbits

Authors

Andrii Dmytryshyn and Bo Kågström

Back Edit this report
Entry responsible: Andrii Dmytryshyn

Page Responsible: Frank Drewes
2024-06-17