
 
 Try the examples in this order. 

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

    Properties of Euclidian inner product in R**n :
    =============================================

                         u.v  = v.u       : euinprdaF.c 
                   (u + v).w  = u.w + v.w : euinprdbF.c
                      (ku).v  = k(u.v)    : euinprdcF.c 
                         u.u >= 0         : euinprddF.c


    If u and v are vector in R**n with the Euclidean inner product : 
    ==============================================================
     
    u.v = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 : thuvF.c


    Cauchy-Schwarz inequality in R**n :  
    =================================

                     |u.v| =< ||u|| ||v|| : causchF.c 


    If u and v are orthogonal in R**n with the Euclidean inner product  : 
    ==================================================================

         ||u+v||**2 = ||u||**2 + ||v||**2 : pythgF.c



    Properties of length in R**n :
    ============================

               ||u + v|| =< ||u|| + ||v|| : lngthcF.c (triangle inequality)


    Properties of distance in R**n :
    ==============================

              d(u,v) >=   0               : distcaF.c 
              d(u,v)  =   d(v,u)          : distccF.c 
              d(u,v)  =<  d(u,w) + d(w,v) : distcdF.c (triangle inequality)
