Brunowsky local form of a holomorphic family of pairs of matrices Original Research Article

Following Arnoldʹs techniques, we obtain a local canonical form of a holomorphic family of pairs of matrices (A(λ), B(λ)) acted 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(0), B(0)). We make some applications to local perturbations of a pair of matrices.