Mathc matrices/c12fn4

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),999.);
double **EigsVector=                   i_mR(r,r);
double **EigsValue =                   i_mR(r,C1);

  clrscrn();
  printf(" The nonzero eigenvalues of a skew-symmetric"
         " matrix are non-real.\n\n");
  printf(" Copy/Past into the octave windows \n\n");
  p_Octave_mR(A,"a",P0);
  printf(" [V, E] = eigs (a,%d) \n\n",r);
   
  f_mR(A);
  f_mR(EigsVector);
  f_mR(EigsValue);
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
 fun(rp_I(R4)+R2);

} while(stop_w());

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

Les valeurs propres d'une matrice anti-symétrique sont imaginaires

Exemple de sortie écran :

 The nonzero eigenvalues of a skew-symmetric matrix are non-real.

 Copy/Past into the octave windows 

 a=[
+0,-157,-703,-879;
+157,+0,+332,-42;
+703,-332,+0,+515;
+879,+42,-515,+0]

 [V, E] = eigs (a,4) 


 Press   return to continue
 Press X return to stop    



 a=[
+0,-157,-703,-879;
+157,+0,+332,-42;
+703,-332,+0,+515;
+879,+42,-515,+0]

>>  [V, E] = eigs (a,4)
V =

   0.6374 +      0i   0.6374 -      0i   0.0961 + 0.2906i   0.0961 - 0.2906i
  -0.1054 - 0.0166i  -0.1054 + 0.0166i   0.6990 +      0i   0.6990 -      0i
  -0.2149 - 0.4646i  -0.2149 + 0.4646i  -0.0434 + 0.4858i  -0.0434 - 0.4858i
   0.1907 - 0.5328i   0.1907 + 0.5328i   0.0161 - 0.4237i   0.0161 + 0.4237i

E =

Diagonal Matrix

-0.00 + 1251.15i                 0                0                 0
               0  -0.00 - 1251.15i                0                 0
               0                 0  0.00 +  321.47i                 0
               0                 0                0   0.00 -  321.47i