
 
 Try the examples in this order. 

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

    Axioms of inner product in M22 :
    ===============================

                         <U,V>  =   <V,U>         : inprdM2a.c 
                     <U + V,W>  =   <U,W> + <V,W> : inprdM2b.c
                        <kU,V>  =  k<U,V>         : inprdM2c.c 
                         <U,U> >=  0              : inprdM2d.c

    Axioms of inner product in Mnn :
    ===============================

                         <U,V>  =   <V,U>         : inprdMna.c 
                     <U + V,W>  =   <U,W> + <V,W> : inprdMnb.c
                        <kU,V>  =  k<U,V>         : inprdMnc.c 
                         <U,U> >=  0              : inprdMnd.c


    Axioms of inner product in Mnm :
    ===============================

                         <U,V>  =   <V,U>         : inprdMpa.c 
                     <U + V,W>  =   <U,W> + <V,W> : inprdMpb.c
                        <kU,V>  =  k<U,V>         : inprdMpc.c 
                         <U,U> >=  0              : inprdMpd.c

    Properties of inner product in Mnm :
    ==================================

                         <0,V>  =   <V,0> =  0    : inprdMpe.c 
                     <U,V + W>  =   <U,V> + <U,W> : inprdMpf.c
                        <U,kV>  =  k<U,V>         : inprdMpg.c 
                     <U - V,W>  =   <U,W> - <V,W> : inprdMph.c
                     <U,V - W>  =   <U,V> - <U,W> : inprdMpi.c


    If u and v are vector in Mnm with the inner product : 
    ===================================================
     
           u.v  = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 :  normMa.c
          |u.v| =< ||u|| ||v||                    : causchM.c


    Properties of distance in Mnm :
    =============================

                      d(u,v) >=   0               : distMa.c 
                      d(u,v)  =   d(v,u)          : distMb.c 
                      d(u,v)  =<  d(u,w) + d(w,v) : distMc.c (triangle inequality)
