The ring of invariants of matrices

Abstract

We denote by M(n) the space of all n × n-matrices with their coefficients in the complex number field C and by G the group of invertible matrices GL(n, C). Let W = M(n)i be the vector space of l-tuples of n × ra-matrices. We denote by ρ: G → GL(W) a rational representation of G defined as follows:if S ∈ G, A(i) ∈ M(n) (i = 1, 2, …, l).