 
 Try the examples in this order. 

 (You can compile the *.c files directly without create a project)

    Axioms of the Weighed Euclidean Inner Product :
    ==============================================

                         <U,V>  =   <V,U>         : inprdWa.c 
                     <U + V,W>  =   <U,W> + <V,W> : inprdWb.c
                        <kU,V>  =  k<U,V>         : inprdWc.c 
                         <U,U> >=  0              : inprdWd.c

    Properties of the Weighed Euclidean Inner Product :
    =================================================

                         <0,V>  =   <V,0> =  0    : inprdWe.c 
                     <U,V + W>  =   <U,V> + <U,W> : inprdWf.c
                        <U,kV>  =  k<U,V>         : inprdWg.c 
                     <U - V,W>  =   <U,W> - <V,W> : inprdWh.c
                     <U,V - W>  =   <U,V> - <U,W> : inprdWi.c


    With of the Weighed Euclidean Inner Product : 
    ===========================================
     
            u.v = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 : normWa.c


    Properties of distance generated by the Weighed Euclidean Inner Product :
    =======================================================================

                      d(u,v) >=   0               : distWa.c 
                      d(u,v)  =   d(v,u)          : distWb.c 
                      d(u,v)  =<  d(u,w) + d(w,v) : distWc.c (triangle inequality)
