Linear Algebra and the C Language/a05u

Install and compile this file in your working directory.

/* ------------------------------------ */
/*  Save as :   c00b.c                  */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
int main(void)
{ 
double u_T[R1*C3] = {    4,   2,   5};                                             
double v_T[R1*C3] = {    3,   4,   1};

double **U_T =        ca_A_mR(u_T,     i_mR(R1,C3));
double **V_T =        ca_A_mR(v_T,     i_mR(R1,C3));

double **UxV_T =       UxV_mR(U_T,V_T, i_mR(R1,C3));  
 
double **U     = transpose_mR(U_T,     i_mR(R3, C1));
double **V     = transpose_mR(V_T,     i_mR(R3, C1));
double **UxV   = transpose_mR(UxV_T,   i_mR(R3, C1));
    
  clrscrn();       
  printf("  u_t:");
  p_mR(U_T, S4, P0, C6);
  printf("  v_t:");
  p_mR(V_T, S4, P0, C6);
  printf("  uxv_t:");
  p_mR(UxV_T, S4, P0, C6);
                  
  printf("                      ||u x v||**2 == %+.4f\n"
         "      ||u||**2 ||v||**2 - (u.v)**2 == %+.4f\n\n", 
         
                           pow(norm_R(UxV),2), 
         
     pow(norm_R(U),2) * pow(norm_R(V),2) - pow(dot_R(U,V),2) ); 
     
  stop();
                 
  f_mR(U_T); 
  f_mR(V_T);
  f_mR(UxV_T);
    
  f_mR(U); 
  f_mR(V);
  f_mR(UxV);   

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

||u x v||**2 == ||u||**2 ||v||**2 - (u.v)**2

Screen output example:

  u_t  :
  +4   +2   +5 

  v_t  :
  +3   +4   +1 

  uxv_t :
 -18  +11  +10 

                      ||u x v||**2 == +545.0000          
      ||u||**2 ||v||**2 - (u.v)**2 == +545.0000        

 Press return to continue.