Miniversal deformations of pairs of skew-symmetric forms

Details Miniversal deformations of pairs of skew-symmetric forms Miniversal deformations of pairs of skew-symmetric forms

2011-04-13

arxiv.org/abs/1104.2492v1

Mathematics

Representation Theory

36 pages

Scientific paper

We give a miniversal deformation of each pair of skew-symmetric matrices $(A,B)$ under congruence; that is, a normal form with minimal number of independent parameters to which all matrix pairs $(A+E,B+E')$ close to $(A,B)$ can be reduced by congruence transformation $ (A+E,B+E')\mapsto {\cal S}(E,E')^T (A+E,B+E') {\cal S}(E,E'), {\cal S}(0,0)=I, $ in which ${\cal S}(E,E')$ smoothly depends on the entries of $E$ and $E'$.

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