Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils Original Research Article

For a family of linear operators image over image that smoothly depend on parameters image, V.I. Arnold obtained the simplest normal form of their matrices relative to a smoothly depending on image change of a basis in U. We solve the same problem for a family of linear operators image over image, for a family of pairs of linear mappings image over image and image, and for a family of pairs of counter linear mappings image over image and image.