Defining relations for the algebra of invariants of 2 x 2 matrices

We obtain defining relations of the algebra of invariants of the classical subgroups of GL(2)(C) acting by simultaneous conjugation on m-tuples of 2 x 2 complex matrices. The sets of defining relations look uniformly for all m greater than or equal to 2 and are derived by translation of classical results on invariant theory of orthogonal groups in the language of 2 x 2 matrix invariants, combined with arguments of representation theory of the general linear group GL(m)(C) and ideas coming from the theory of algebras with polynomial identities.