Brunowsky local form of a holomorphic family of pairs of matrices

Following Arnold’s techniques, we obtain a local canonical form of a holomorphic family of pairs of matrices ( A( A), B(h)) ac t e d on by the state feedback group. We obtain an explicit formula to compute the dimension of the base space of any miniversal deformation of ( A(O), B(O)). W e m ak e some applications to local perturbations of a pair of matrices.