Linear Algebra and the C Language/a0n1

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as:  c00a.c                    */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A         = rsymmetric_mR(      i_mR(r,r),9);
double **InvA      =      invgj_mR(A,    i_mR(r,r));

double **AEVect    =     eigs_V_mR(A,    i_mR(r,r));
double **InvAEVect =     eigs_V_mR(InvA, i_mR(r,r));

  clrscrn();   
  printf(" A:");
  p_mR(A, S10,P4,C6);

  printf(" InvA:");
  p_mR(InvA, S10,P4,C6);
  stop();
  
  clrscrn();   
  printf(" The matrix A and the matrix InvA\n"
         " have the same eingvectors. They \n"
         " are in reverse order.       \n\n\n"

         " The eigenvectors of A being     \n"
         " an orthonormal matrix, we       \n"
         " will simply take its transpose  \n"
         " as inverse in the next files. \n\n"
         " EigenVector of A:");
  p_mR(AEVect,S10,P4,C6);

  printf(" EigenVector of InvA:");
  p_mR(InvAEVect,S10,P4,C6);
   
  f_mR(A);
  f_mR(InvA); 
  f_mR(AEVect);
  f_mR(InvAEVect);  
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
 fun(R3);

} while(stop_w());

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

To calculate the spectral decomposition of matrix A. We  need the eigenvectors and eigenvalues of matrix A and the eigenvectors of the inverse of A.

The eigenvectors of A being an orthonormal matrix, we will  take its transpose as inverse in the next files.

Screen output example:

                                                                                       
 A:
   -5.0000    +4.0000    -2.0000 
   +4.0000    +2.0000    -2.0000 
   -2.0000    -2.0000    +5.0000 

 InvA:
   -0.0698    +0.1860    +0.0465 
   +0.1860    +0.3372    +0.2093 
   +0.0465    +0.2093    +0.3023 

 Press return to continue. 


 The matrix A and the matrix InvA
 have the same eingvectors. They 
 are in reverse order.       


 The eigenvectors of A being     
 an orthonormal matrix, we       
 will simply take its transpose  
 as inverse in the next files.

 EigenVector of A:
   -0.3066    +0.9159    +0.2592 
   -0.5409    -0.3917    +0.7443 
   +0.7832    +0.0881    +0.6155 

 EigenVector of InvA:
   +0.2592    +0.9159    -0.3066 
   +0.7443    -0.3917    -0.5409 
   +0.6155    +0.0881    +0.7832 


 Press   return to continue
 Press X return to stop