MATB24H3 Lecture : Lecture11.pdf
Document Summary
Review from mata23: for all v, w and u rn we have v u is the real number given by: v u = v1u1 + v2u2 + + vnun. We also know that the following properties are satis ed: if v, u, w . On other vector spaces we may de ne an analogous product that satis es the above properties and call it inner product. We will use the notation < v, u > for the inner product of the vectors v, u. Definition: an inner product on a real vector space v is a function that associates a real number < v, u > with each pair of vectors v and u in. V such that the following are satis ed v, u, w v and scalars r : A vector space together with an inner product de ned on it is called an inner product space. Example: in the vector space r2 verify that.
