Mathc complexes/a237

Application

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	c00b.c

/* ------------------------------------ */
/*  Save as : c01b.c                    */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define   RB R2
#define   CB C2

#define   RU R2
#define   CU C1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double   b[RB*(CB*C2)]={
    +2, 2,   +1, 5,  
    +2, 0,   +3, 5       
};

double u_s[RU*(CU*C2)]={
        -13, +5, 
        -13, -3 
};

double **B    = ca_A_mZ(  b, i_mZ(RB,CB));
double **invB = ca_A_mZ(  b, i_mZ(RB,CB));
double **U_s  = ca_A_mZ(u_s, i_mZ(RU,CU));
double **U_b  =              i_mZ(RU,CU) ;

  clrscrn();
  printf(" B is the change of basis matrix for \"B\" \n\n"
         " Find the coordinate of U in the \"B\" basis.\n\n"
         " B :  ");
  p_mZ(B, S4,P0, S3,P0, C7);
  printf(" U_s :   the coordinate of U in the Standard basis");
  p_mZ(U_s, S4,P0, S3,P0, C7);

  printf(" invB : ");
  p_mZ(inv_mZ(B,invB), S8,P4, S8,P4, C7);
  printf("         invB*U_s = U_b \n\n"
         " U_b :   the coordinate of U in the \"B\" basis");
  p_mZ(mul_mZ(invB,U_s,U_b), S6,P1, S6,P1, C7);
  stop();

  f_mZ(U_s);
  f_mZ(U_b);
  f_mZ(B);
  f_mZ(invB);
    
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Matrice de passage inversible :

Soit B la matrice de changement de base de B 

Trouver les coordonnées de U dans la base B  : 

       B * U_b = U_s         
  invB B * U_b = invB U_s
           U_b = invB U_s   
                  

Exemple de sortie écran :

 ------------------------------------ 
 B is the change of basis matrix for "B" 

 Find the coordinate of U in the "B" basis.

 B :  
  +2 +2i   +1 +5i 
  +2 +0i   +3 +5i 

 U_s :   the coordinate of U in the Standard basis
 -13 +5i 
 -13 -3i 

 invB : 
 +0.1667 -0.6667i  -0.3333 +0.5000i 
 +0.1667 +0.1667i  -0.0000 -0.3333i 

         invB*U_s = U_b 

 U_b :   the coordinate of U in the "B" basis
  +7.0  +4.0i 
  -4.0  +3.0i 

 Press return to continue.