% 	SPANNING: THE OUTER PRODUCTGAfigure; clc; %/% 	SPANNING: THE OUTER PRODUCT%global v w; %/clf; %/% 	The outer product is anti-symmetric:%e1^e2 %we2^e1 %we1^e1 %wGAprompt; %/% 	and the outer product is linear:%.e1^(e2+e3) %w%	All bivectors expressible on BIVECTOR BASIS.%.% 	Those properties yield certain identities:%.e1^(e1+e2) %wGAprompt; %/%% Now let us draw these bivectors%.v = e1 + e2;w = e2 + 2*e3;B = 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; %/ %	Again, the actual object is coordinate-free.axis off; %/GAprompt; %/GAorbiter(380,10); %/% 	The bivector v^w has dimension, direction, %	sense and area, but NO SHAPEGAprompt; %/va = [-1.5 2.5 -0.75 3.5 -1 2]; %/axis(va); %/% 	(a more distant view)');GAprompt; %/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; %/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; %/%	(Note that all points spanning same bivector with v%	are on a line parallel to v)%GAprompt; %/% 	If no spanning vectors are known %	we draw the bivector as a disk:%.draw(v^w,'g'); GAtext(-0.2*unit((v^w)*I3)-w/4,'v \wedge w'); %/ axis(va); %/GAprompt; %/GAorbiter(360,10); %/