
                                                            freeware xhunga@tiscali.fr  
     Vector :
     ******
        
  a) Verify with numeric applications.

     * Properties of Euclidian inner product in R**n.
     * Properties of length   in R**n.
     * Properties of distance in R**n.
     * u.v = 1/4 ||u+v||**2  -  1/4 ||u-v||**2. 
     * Cauchy-Schwarz inequality in R**n.
     * If u.v =0 :  ||u+v||**2 = ||u||**2 + ||v||**2.

  b) The coefficients, integers or fractions, are randomly
     selected by the computer.

  c) The size of the vectors, are randomly selected by the 
     computer, but you can selecte  the size  if you want.
   
      I have used gcc.2.9 (Dev-C++ 4), 
                  gcc.3.2 (v2DJGPP Rhide).

        The list of all  the programs : aaprogr.txt
        Save your work in a text file : aaasave.txt
        ShortName  For  The  Matrices : aashtnm.txt

        The list of all the matrix packages : aapakmt.txt
        The list of all the vector packages : aapakvt.txt
