 
 Try the examples in this order. 

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

   Find the associated normal sytem of the linear system Ax = b : AssNormSystR.c                 
   Find the least squares solution of the linear system  Ax = b :   leastsqrsR.c
   Find the orthogonal projection of b on the column space of A :  OrthProjwbR.c

         A has linearly independent column vectors.  
                          <=>                         
                 (A**T A) is invertible :                                 AT_A.c

         Verify that the error vector Ax - b resulting from
            the least squares solution x is orthogonal 
                  to the column space of A (Acn) :                errvectAxmnb.c

   A square matrix A with property invA = A**T 
       is said to be orthogonal matrix :                               orthmAR.c orthmA3.c 

          A an n x n orthogonal matrix.  
   The column vectors of A form an orthonormal set in R**n 
         With the euclidean inner product :                            orthmBR.c orthmB3.c 

             A an n x n orthogonal matrix. 
    The row vectors of A form an orthonormal set in R**n 
            With the euclidean inner product :                         orthmCR.c orthmC3.c 

          A an n x n orthogonal matrix.
            det(A) = 1 or det(A) = -1 :                                orthmER.c orthmE3.c 

        The multiplication by an orthonormal matrix A  
          leave the lenghs of all vectors unchanged:                   orthmFR.c orthmF3.c 

         If A is the transition matrix from a basis   
           B' to a basis B. InvA is the transition     
                 matrix  from B to B' :                                orthmGR.c orthmG3.c 