disp('>> % 	SPANNING: THE OUTER PRODUCT');     % 	SPANNING: THE OUTER PRODUCT     GAfigure; clc; %/     disp('>> % 	SPANNING: THE OUTER PRODUCT');     % 	SPANNING: THE OUTER PRODUCT     disp('>> %');     %     global v w; %/     clf; %/     disp('>> % 	The outer product is anti-symmetric:');     % 	The outer product is anti-symmetric:     disp('>> %');     %     fprintf(1,'>> e1^e2  ');     input('');     e1^e2 %w     fprintf(1,'>> e2^e1  ');     input('');     e2^e1 %w     fprintf(1,'>> e1^e1  ');     input('');     e1^e1 %w     GAprompt; %/     disp('>> % 	and the outer product is linear:');     % 	and the outer product is linear:     fprintf(1,'\n');     fprintf(1,'>> e1^(e2+e3)  ');     input('');     e1^(e2+e3) %w     disp('>> %	All bivectors expressible on BIVECTOR BASIS.');     %	All bivectors expressible on BIVECTOR BASIS.     fprintf(1,'\n');     disp('>> % 	Those properties yield certain identities:');     % 	Those properties yield certain identities:     fprintf(1,'\n');     fprintf(1,'>> e1^(e1+e2)  ');     input('');     e1^(e1+e2) %w     GAprompt; %/     disp('>> %');     %     disp('>> % Now let us draw these bivectors');     % Now let us draw these bivectors     fprintf(1,'\n');     disp('>> v = e1 + e2;');     v = e1 + e2;     disp('>> w = e2 + 2*e3;');     w = e2 + 2*e3;     disp('>> B = v^w;');     B = v^w;     disp('>> DrawBivector(v,w);');     DrawBivector(v,w);     GAview([30 30]); %/     GAtext(0.5*v-0.1*unit(w)+0.1*unit(grade(((v^w)/I3),1)),'v'); %/     GAtext(0.5*w+0.1*unit(v)+0.1*unit(grade(((v^w)/I3),1))+v,'w'); %/     GAtext(0.5*v+0.7*w-0.2*unit((v^w)*I3),'v \wedge w'); %/     axis('vis3d'); %/     GAprompt; %/      disp('>> %	Again, the actual object is coordinate-free.');     %	Again, the actual object is coordinate-free.     axis off; %/     GAprompt; %/     GAorbiter(380,10); %/     disp('>> % 	The bivector v^w has dimension, direction, ');     % 	The bivector v^w has dimension, direction,      disp('>> %	sense and area, but NO SHAPE');     %	sense and area, but NO SHAPE     GAprompt; %/     va = [-1.5 2.5 -0.75 3.5 -1 2]; %/     axis(va); %/     disp('>> % 	(a more distant view)'');');     % 	(a more distant view)');     GAprompt; %/     disp('>> DrawBivector(v,1.5*v+w); ');     DrawBivector(v,1.5*v+w);      GAtext(0.5*v+0.7*(1.5*v+w)-0.2*unit((v^w)*I3),'v \wedge w');  %/     axis(va); %/     GAprompt; %/     disp('>> DrawBivector(v,-1.5*v+w); ');     DrawBivector(v,-1.5*v+w);      GAtext(0.5*v+0.7*(-1.5*v+w)-0.2*unit((v^w)*I3),'v \wedge w'); %/     axis(va); %/     GAprompt; %/     GAorbiter(360,10); GAprompt; %/     disp('>> %	(Note that all points spanning same bivector with v');     %	(Note that all points spanning same bivector with v     disp('>> %	are on a line parallel to v)');     %	are on a line parallel to v)     disp('>> %');     %     GAprompt; %/     disp('>> % 	If no spanning vectors are known ');     % 	If no spanning vectors are known      disp('>> %	we draw the bivector as a disk:');     %	we draw the bivector as a disk:     fprintf(1,'\n');     disp('>> draw(v^w,''g''); ');     draw(v^w,'g');      GAtext(-0.2*unit((v^w)*I3)-w/4,'v \wedge w'); %/      axis(va); %/     GAprompt; %/     GAorbiter(360,10); %/