Given two real vectors in [tex](u_1,\ldots,u_n)[/tex] and [tex](v_1,\ldots,v_n)[/tex], does the pointwise-product (elementwise-product) [tex](u_1v_1,\ldots,u_nv_n)[/tex] have a geometrical meaning? or can it at least be expressed as a combination of other known products (e.g. outer-product, contraction, and so on...)?