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Mathc matrices/a234
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c01a.c */
void fun(int r)
double **u = r_mR( i_mR(r,C1),9.);
double **v = r_mR( i_mR(r,C1),9.);
clrscrn();
printf(" u :");
p_mR(u,S3,P0,C6);
printf(" v :");
p_mR(v,S3,P0,C6);
printf(" Cauchy-Schwarz : |<u,v>| <= ||u|| ||v|| \n\n"
" |<u,v>| = %+.0f\t ||u|| ||v|| = %+.0f\n\n\n"
" |<u,v>|\t <= ||u|| ||v|| \n"
" %+.0f\t <= %+.0f \n",
fabs( dot_uv_R(u, v)),
norm_uv_R(u) * norm_uv_R(v),
fabs( dot_uv_R(u, v)),
norm_uv_R(u) * norm_uv_R(v) );
f_mR(u);
f_mR(v);
/* ------------------------------------ */
int main(void)
time_t t;
srand(time(&t));
do
fun(rp_I(R3)+R2);
} while(stop_w());
return 0;
/* ------------------------------------ */
Nous vérifions une des propriétés de la norme : norm_uv_R(u);
Exemple de sortie écran :
u :
+7
+4
+9
+6
-4
v :
+8
-2
+6
+9
+7
Cauchy-Schwarz : |<u,v>| <= ||u|| ||v||
|<u,v>| = +128 ||u|| ||v|| = +215
|<u,v>| <= ||u|| ||v||
+128 <= +215
Press return to continue
Press X return to stop
Mathc matrices/a235
Propriétés
u x v :
u x v == - v x u :
u x (v+w) == (uxv) + (uxw) :
(v+w) x u == (vxu) + (wxu):
s (uxv) == su x v == u x sv :
If u and v are colinear then u x v == 0 :
u.(u x v) == 0 :
u.(u x v) == det(A) == 0 :
Mathc matrices/a236
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c00a.c */
void fun(void)
double **U_T = r_mR(i_mR(R1, C3), 9);
double **V_T = r_mR(i_mR(R1, C3), 9);
double **A = rp_mR(i_mR(R3, C3), 1);
double **B = rp_mR(i_mR(R3, C3), 1);
c_r_mR(U_T, R1, A, R2);
c_r_mR(V_T, R1, A, R3);
c_r_mR(V_T, R1, B, R2);
c_r_mR(U_T, R1, B, R3);
clrscrn();
printf(" u_T :");
p_mR(U_T, S3, P0, C6);
printf(" v_T :");
p_mR(V_T, S3, P0, C6);
printf("\n u x v == -v x u C* = cofactors \n\n"
" u x v = (C11, C12, C13) = (%+.0f, %+.0f, %+.0f) \n"
" v x u = (C11, C12, C13) = (%+.0f, %+.0f, %+.0f)\n\n",
cofactor_R(A, R1, C1),
cofactor_R(A, R1, C2),
cofactor_R(A, R1, C3),
cofactor_R(B, R1, C1),
cofactor_R(B, R1, C2),
cofactor_R(B, R1, C3) );