Mathc complexes/a251

Application

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	c04b.c

/* ------------------------------------ */
/*  Save as :   c04b.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define   RAT R2
#define   CAT C4
#define   Cb C1
/* ------------------------------------ */
int main(void)
{
double a_Tb[RAT*((CAT+Cb)*C2)]={
 -2,+3, +1,+0, +0,-1, 3,-5, +0,+0,
 -4,+2, -3,+5, -6,+4,-1,+0, +0,+0 
};
 
double **ATb =   ca_A_mZ(a_Tb, i_Abr_Ac_bc_mZ(RAT,CAT,Cb));
double **AT  = c_Ab_A_mZ(ATb,  i_mZ(RAT,CAT));
double **b   = c_Ab_b_mZ(ATb,  i_mZ(RAT,Cb));

  clrscrn();
  printf(" Verify if AT is Basis for a Row Space by Row Reduction :\n\n");
  printf(" AT :");
  p_mZ(AT,S6,P1,S6,P1,C10);
  printf(" b :");
  p_mZ(b,S6,P1,S6,P1,C10);
  printf(" ATb :");
  p_mZ(ATb,S6,P1,S6,P1,C10);
  stop();

  clrscrn();
  printf(" The nonzero row vectors of ATb form a basis\n"
         " for the row space of AT, and hence form a \n"
         " basis for the column space of A \n\n"
         " ATb :");
  p_mZ(ATb,S7,P3,S7,P3,C10);
  printf(" ATb :  gj_PP_mZ(ATb) :");
  gj_PP_mZ(ATb);
  p_mZ(ATb,S7,P3,S7,P3,C10);
  stop();
   
  f_mZ(ATb);
  f_mZ(b);
  f_mZ(AT);
  
  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Trouver une projection sur un sous-espace vectoriel par une application linéaire :

• Dans cet exemple nous vérifions si les vecteurs lignes de AT sont linéairement indépendant. Il ne doit pas y avoir des lignes de zéro.

Exemple de sortie écran :

 ------------------------------------ 
 Verify if AT is Basis for a Row Space by Row Reduction :

 A_T :
  -2.0  +3.0i   +1.0  +0.0i   +0.0  -1.0i   +3.0  -5.0i 
  -4.0  +2.0i   -3.0  +5.0i   -6.0  +4.0i   -1.0  +0.0i 

 b :
  +0.0  +0.0i 
  +0.0  +0.0i 

 A_Tb :
  -2.0  +3.0i   +1.0  +0.0i   +0.0  -1.0i   +3.0  -5.0i   +0.0  +0.0i 
  -4.0  +2.0i   -3.0  +5.0i   -6.0  +4.0i   -1.0  +0.0i   +0.0  +0.0i 

 Press return to continue. 


 ------------------------------------ 
 The nonzero row vectors of A_Tb form a basis
 for the row space of A_T, and hence form a 
 basis for the column space of A 

 A_Tb :
 -2.000 +3.000i  +1.000 +0.000i  +0.000 -1.000i  +3.000 -5.000i  +0.000 +0.000i 
 -4.000 +2.000i  -3.000 +5.000i  -6.000 +4.000i  -1.000 +0.000i  +0.000 +0.000i 

 A_Tb :  gj_PP_mZ(A_Tb) :
 +1.000 +0.000i  +1.100 -0.700i  +1.600 -0.200i  +0.200 +0.100i  +0.000 -0.000i 
 +0.000 +0.000i  +1.000 -0.000i  +1.373 +0.232i  +1.264 +0.491i  +0.000 +0.000i 

 Press return to continue.