%
% Valores Singulares
%
% SEM 5928 - Sistemas de Controle 
% Escola de Engenharia de São Carlos - USP
%
% Adriano Siqueira - 2016
%

G=[5 4;3 2];

figure
subplot(1,2,1)
hold on
axis([-1.2 1.2 -1.2 1.2])
subplot(1,2,2)
axis([-7.5 7.5 -7.5 7.5])
hold on
for i=0:2*pi/100:2*pi;
d = [cos(i); sin(i)];
subplot(1,2,1)
plot([0 d(1)],[0 d(2)],'b')

y = G*d;
subplot(1,2,2)
plot([0 y(1)],[0 y(2)],'b')

pause(.2)
end

[U,S,V]=svd(G);

subplot(1,2,1)
plot([0 V(1,1)],[0 V(2,1)],'g')

subplot(1,2,2)
plot([0 S(1,1)*U(1,1)],[0 S(1,1)*U(2,1)],'g')

subplot(1,2,1)
plot([0 V(1,2)],[0 V(2,2)],'r')

subplot(1,2,2)
plot([0 S(2,2)*U(1,2)],[0 S(2,2)*U(2,2)],'r')

Scheck = sqrt(eig(G'*G));