SIMULTANEOUS INVARIANTS IN SYSTEMS OF 2ND-ORDER AND 4TH-ORDER TENSORS

Following Hilbert's Theorem [1] to each system of tensors there exists an integrity basis, i.e. a bounded number of invariants such that every arbitrary invariant can be represented as an entire rational function of the elements of this integrity basis. Besides of the invariants of the single tensors to an integrity basis of a system of tensors also belong simultaneous invariants, i.e. invariants being formed of the coordinates of several tensors. In the present paper irreducible systems of simultaneous invariants are constructed are discussed for tensors of orders two and four in the two-, three-, and four-dimensional spaces.