I was wondering if there is such a vector space which is both a Hilbert and affine? I've seen the definition of an Euclidian affine space, which is:
An affine space (A, V, φ) is a Euclidean affine space if the vector space V is a Euclidean vector space.
Thus, it makes me think that an affine space would be a Hilbertian affine space if the vector space V is a Hilbertian vector space. Is this right? or is there any incompatibility between both spaces (affine and Hilbert spaces)?