Mathc matrices/h08a

Matrices anti-symétriques

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A           = rskewsymmetric_mR(                  i_mR(r,r),9);
double **ID          =            eye_mR(                  i_mR(r,r));
double **IDplsA      =            add_mR(ID,A,             i_mR(r,r));
double **invIDplsA   =            inv_mR(IDplsA,           i_mR(r,r));
double **A_invIDplsA =            mul_mR(IDplsA,invIDplsA, i_mR(r,r));

  clrscrn();
  printf(" A ");  
  p_mR(A, S7,P3, C6);
     
  printf(" inv(ID+A) ");
  p_mR(invIDplsA, S7,P3, C6);
   
  printf(" (ID+A) * inv(ID+A) ");
  p_mR(A_invIDplsA , S7,P3, C6);
  
  f_mR(A);
  f_mR(ID);
  f_mR(IDplsA);
  f_mR(invIDplsA);
  f_mR(A_invIDplsA);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
  fun(rp_I(R2)*R2);

} while(stop_w());

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

Si A est une matrice anti-symétrique, alors ID + A est inversible

Exemple de sortie écran :

 A 
 +0.000  +8.000  +2.000  -4.000 
 -8.000  +0.000  -3.000  +7.000 
 -2.000  +3.000  +0.000  +9.000 
 +4.000  -7.000  -9.000  +0.000 

 inv(ID+A) 
 +0.027  -0.118  +0.098  +0.056 
 +0.131  +0.020  +0.040  +0.027 
 -0.093  -0.071  +0.025  -0.105 
 -0.027  -0.025  +0.117  +0.015 

 (ID+A) * inv(ID+A) 
 +1.000  +0.000  -0.000  -0.000 
 -0.000  +1.000  +0.000  +0.000 
 -0.000  +0.000  +1.000  +0.000 
 +0.000  -0.000  +0.000  +1.000 


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