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Miniversal deformations for pairs of skew-symmetric matrices under congruenceare constructed. To be precise, for each such a pair $(A,B)$ we provide anormal form with a minimal number of independent parameters to which all pairsof skew-symmetric matrices $(\widetilde{A},\widetilde{B})$, close to $(A,B)$can be reduced by congruence transformation which smoothly depends on theentries of the matrices in the pair $(\widetilde{A},\widetilde{B})$. An upperbound on the distance from such a miniversal deformation to $(A,B)$ is derivedtoo. We also present an example of using miniversal deformations for analyzingchanges in the canonical structure information (i.e. eigenvalues and minimalindices) of skew-symmetric matrix pairs under perturbations.

Miniversal deformations of pairs of skew-symmetric matrices under congruence