ABSTRACT
An inner product on set V is a function that maps ordered pairs (x,y) from V ×V (that is x and y are elements of V ) to a number < x,y > while satisfying the following properties:
1. For all v in V , < v,v > ≥ 0 and < v,v >= 0 if and only if v = 0. 2. For all u, v, and w in V , < u,v + w >=< u,v > + < u,w >.
