Linear Algebra and the C Language/a0i4

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as :   c00e.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(R4)+R1);

} while(stop_w());

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

If A is an anti-symmetric matrix, then ID + A is invertible

Screen output example:

                                                                                       
 A:
 +0.000  -8.000  +8.000 
 +8.000  +0.000  -4.000 
 -8.000  +4.000  +0.000 

 inv(ID+A):
 +0.117  +0.276  +0.166 
 +0.166  +0.448  +0.469 
 +0.276  +0.414  +0.448 

 (ID+A) inv(ID+A):
 +1.000  +0.000  +0.000 
 +0.000  +1.000  +0.000 
 +0.000  +0.000  +1.000 


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