Tensor fundamental theorems of invariant theory

The aim of this paper is to establish a first and second fundamental theorem for $GL(V)$ equivariant polynomial maps from $k$–tuples of matrix variables $End(V{)}^k$ to tensor spaces $End(V{)}^{\otimes n}$ in the spirit of H. Weyl’s book {\em The classical groups} \cite{Weyl} and of symbolic algebra.