Mathc matrices/08x

Application

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00c.c

/* ------------------------------------ */
/*  Save as :   c00c.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */     
#define RCA          RC3  
/* ------------------------------------ */       
/* ------------------------------------ */
int main(void)
{                          
double a[RCA*RCA] ={   
+2.363636363638, -1.909090909092, -0.272727272727, 
+1.818181818184, -1.545454545456, -0.363636363636, 
-0.909090909092, +1.272727272728, +1.181818181818      
};

double NVN[RCA*RCA] ={   
+0.784464540553, -0.408248290464, -0.557086014531, 
+0.588348405415, -0.408248290464, -0.742781352708, 
-0.196116135138, +0.816496580928, +0.371390676354 
};
                       
double **A      =   ca_A_mR(a,  i_mR(RCA,RCA));
double **Nvn    =  ca_A_mR(NVN, i_mR(RCA,RCA));
double **invNvn = invgj_mR(Nvn, i_mR(RCA,RCA));
double **EValue =               i_mR(RCA,RCA);

double **T      =               i_mR(RCA,RCA);

  clrscrn();
  printf(" A :");
  p_mR(A, S9,P12, C4); 
  
  printf(" Nvn :");
  p_mR(Nvn, S9,P12, C4); 
 
  printf(" Verify if:\n\n"
         " EValue = invNvn * A * Nvn\n\n"
         " EValue  1       EValue  2       EValue  3");
  mul_mR(invNvn,A,T);
  mul_mR(T,Nvn,EValue);
  p_mR(EValue, S9,P12, C4); 
  stop();
  
  clrscrn(); 
  printf(" A :");
  p_mR(A, S9,P12, C4);
            
  printf(" Verify if:\n\n"
         " A = Nvn EValue invNvn");
  mul_mR(Nvn,EValue,T);
  mul_mR(T,invNvn,A); 
  p_mR(A, S8,P12, C3);
  stop();
  
  clrscrn();        
  printf(" det(Nvn)  = %.3e\n"
         " det(Nvn) != 0 V1 and V2 and V3 are linearly independent\n\n",
         det_R(Nvn));  
                    
  printf(" The matrix A projects the space in the direction\n"
         " of the  eigenvector V3  on a plan  determined by\n"
         " the eigenvector V1 and V2 if :\n\n"
         " The eigenvector V1 has its eigenvalue equal to  one and   \n"
         " The eigenvector V2 has its eigenvalue equal to  one and   \n"
         " The eigenvector V3 has its eigenvalue equal to zero and \n\n"
         " If The vectors V1 and V2 and V3 are linearly independent\n\n");         
  stop();  
  
  f_mR(A);
  f_mR(Nvn);  
  f_mR(invNvn);  
  f_mR(T);  
  f_mR(EValue);

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

 Vous vérifiez les propriétés de la matrice A.

* Les valeurs propres : EValue = invNlv A Nlv
* La matrice :               A = Nvn EValue invNvn

Si les vecteurs colonnes de A sont linéairement indépendants

Exemple de sortie écran :

                                                       
 A :
+2.363636363638 -1.909090909092 -0.272727272727 
+1.818181818184 -1.545454545456 -0.363636363636 
-0.909090909092 +1.272727272728 +1.181818181818 

 Nvn :
+0.784464540553 -0.408248290464 -0.557086014531 
+0.588348405415 -0.408248290464 -0.742781352708 
-0.196116135138 +0.816496580928 +0.371390676354 

 Verify if:

 EValue = invNvn * A * Nvn

 EValue  1       EValue  2       EValue  3
+1.000000000000 +0.000000000000 +0.000000000000 
+0.000000000000 +1.000000000000 +0.000000000000 
-0.000000000000 +0.000000000000 +0.000000000000 

 Press return to continue. 


 A :
+2.363636363638 -1.909090909092 -0.272727272727 
+1.818181818184 -1.545454545456 -0.363636363636 
-0.909090909092 +1.272727272728 +1.181818181818 

 Verify if:

 A = Nvn EValue invNvn
+2.363636363638 -1.909090909092 -0.272727272727 
+1.818181818184 -1.545454545456 -0.363636363636 
-0.909090909092 +1.272727272728 +1.181818181818 

 Press return to continue. 


 det(Nvn)  = 1.635e-01
 det(Nvn) != 0 V1 and V2 and V3 are linearly independent

 The matrix A projects the space in the direction
 of the  eigenvector V3  on a plan  determined by
 the eigenvector V1 and V2 if :

 The eigenvector V1 has its eigenvalue equal to  one and   
 The eigenvector V2 has its eigenvalue equal to  one and   
 The eigenvector V3 has its eigenvalue equal to zero and 

 If The vectors V1 and V2 and V3 are linearly independent

 Press return to continue.