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UMINF 15.16

Structure preserving stratification of skew-symmetric matrix polynomials

We study how elementary divisors and minimal indices of a skew-symmetric matrix polynomial of odd degree may change under small perturbations of the matrix coecients. We investigate these changes qualitatively by constructing the strati cations (closure hierarchy graphs) of orbits and bundles for skew-symmetric linearizations. We also derive the necessary and sucient conditions for the existence of a skew-symmetric matrix polynomial with prescribed degree, elementary divisors, and minimal indices.

Keywords

bundle, canonical structure information, matrix polynomials, orbit, skew-symmetric matrix pencils, skew-symmetric matrix polynomials, stratifications

Authors

Andrii Dmytryshyn

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Entry responsible: Andrii Dmytryshyn

Page Responsible: Frank Drewes
2022-09-30