The ring of invariants of matrices

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 ).

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