Consider the component-wise action of the group $SO(p)\times SO(q)$ in the tensor product of two real vector spaces $S^2(R^p)\otimes R^q$. How to parametrize orbits of this action ? For $q=1$ we obtain a nice answer: the parameters are eigenvalues of the bilinear form.
Ring of invariants for the action of rotation groups in tensors.
1
$\begingroup$
multilinear-algebra
geometric-group-theory
invariant-theory
-
0$R^p$ - the standard p-dimensional inner product space, $S^2 (R^P)$ - the second symmetric power of $R^p$, or the space of symmetric bilinear forms of $R^p$, here the duality doesn't matter. – 2012-11-07