For each pair of complex symmetric matrices (A,B) we provide a normal form
with a minimal number of independent parameters, to which all pairs of complex
symmetric matrices (A,B), close to (A,B) can be
reduced by congruence transformation that smoothly depends on the entries of
A and B. Such a normal form is called a miniversal
deformation of (A,B) under congruence. A number of independent parameters in
the miniversal deformation of a symmetric matrix pencil is equal to the
codimension of the congruence orbit of this symmetric matrix pencil and is
computed too. We also provide an upper bound on the distance from (A,B) to
its miniversal deformation.Comment: arXiv admin note: text overlap with arXiv:1104.249