
 
 Try the examples in this order. 

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

    Axioms of Inner Product on R**n generated by A :
    ==============================================

                         <U,V>  =   <V,U>         : inprdAa.c 
                     <U + V,W>  =   <U,W> + <V,W> : inprdAb.c
                        <kU,V>  =  k<U,V>         : inprdAc.c 
                         <U,U> >=  0              : inprdAd.c

    Properties of Inner Product on R**n generated by A :
    ==================================================

                         <0,V>  =   <V,0> =  0    : inprdAe.c 
                     <U,V + W>  =   <U,V> + <U,W> : inprdAf.c
                        <U,kV>  =  k<U,V>         : inprdAg.c 
                     <U - V,W>  =   <U,W> - <V,W> : inprdAh.c
                     <U,V - W>  =   <U,V> - <U,W> : inprdAi.c


    With Inner Product on R**n generated by A : 
    =========================================
     
            u.v = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 : normAa.c


    Properties of distance on R**n generated by A :
    =============================================

                      d(u,v) >=   0               : distAa.c 
                      d(u,v)  =   d(v,u)          : distAb.c 
                      d(u,v)  =<  d(u,w) + d(w,v) : distAc.c (triangle inequality)
