Transvectant

In mathematical invariant theory, a transvectant is an invariant formed from "n" invariants in "n" variables using Cayley's Ω process.
Definition.
If "Q"1...,"Q""n" are functions of "n" variables x = ("x"1...,"x""n") and "r" ≥ 0 is an integer then the "r"th transvectant of these functions is a function of "n" variables given by
where Ω is Cayley's Ω process, the tensor product means take a product of functions with different variables x1..., x"n", and tr means set all the vectors x"k" equal.
Examples.
The zeroth transvectant is the product of the "n" functions.
The first transvectant is the Jacobian determinant of the "n" functions.
The second transvectant is a constant times the completely polarized form of the Hessian of the "n" functions.