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. The developed theory relies on our main theorem stating that a skew-symmetric matrix pencil A-λB can be approximated by pencils strictly equivalent to a skew-symmetric matrix pencil C-λD if and only if A-λB can be approximated by pencils congruent to C-λD.
CITATION STYLE
Dmytryshyn, A., & Kågström, B. (2014). Orbit closure hierarchies of skew-symmetric matrix pencils. SIAM Journal on Matrix Analysis and Applications, 35(4), 1429–1443. https://doi.org/10.1137/140956841
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