Let A be an algebra over complex numbers with an antilinear automorphism ?, M be a bimodule over A. A positive definite Hermitian form (·, ·) on M is said to be invariant if (am, n) = (m, n?(a)) for all a ? A, m,n ? M. I will discuss classification of positive definite invariant forms in the following cases: (1) M = A and A is a non-commutative deformation of a Kleinian singularity of type A, sometimes called generalized Weyl algebra. (2) M = A and A is a q-deformation of a Kleinian singularity of type A (generalized q-Weyl algebra). (3) A is a Weyl or a q-Weyl algebra with generic parameter. The first case is joint work with Etingof, Rains, Stryker.