A note on finite determinacy of matrices

Abstract

In this note, we give a necessary and sufficient condition for a matrix A in M(2,2) to be finitely G-determined, where M(2,2) is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M(2,2) by change of coordinates together with multiplication by invertible matrices from both sides.