clear
close all

lambda1 = -2;
lambda2 = 4;
Lambda = diag([lambda1;lambda2]);

v1 = [1;1];
v2 = [1;-1];
T = [v1,v2];

A = T*Lambda*inv(T);

[Z1,Z2] = meshgrid(-10:1:10,-10:1:10);
Uz = lambda1*Z1;
Vz = lambda2*Z2;
subplot(1,2,2)
quiver(Z1,Z2,Uz,Vz);
xlabel('z_1')
ylabel('z_2')
axis([-10,10,-10,10])
axis square
hold on

[X1,X2] = meshgrid(-10:1:10,-10:1:10);
Ux = A(1,1)*X1+A(1,2)*X2;
Vx = A(2,1)*X1+A(2,2)*X2;
subplot(1,2,1)
quiver(X1,X2,Ux,Vx);
xlabel('x_1')
ylabel('x_2')
axis([-10,10,-10,10])
axis square
hold on

t = [0:0.01:1]';
for theta = 0:pi/8:2*pi
z0 = 5*[cos(theta);sin(theta)];

z1 = exp(lambda1*t)*z0(1);
z2 = exp(lambda2*t)*z0(2);

figure(1)
subplot(1,2,2)
plot(z1(1),z2(1),'ro',z1,z2,'r')
hold on

x = z1*v1'+z2*v2';
x1 = x(:,1);
x2 = x(:,2);

subplot(1,2,1)
plot(x1(1),x2(1),'ro',x1,x2,'r')
hold on

figure(2)
subplot(2,2,2)
plot(t(1),z1(1),'ro',t,z1,'r')
ylabel('z_1(t)')
xlabel('t (s)')
axis([0 1 -20 20])
hold on
subplot(2,2,4)
plot(t(1),z2(1),'ro',t,z2,'r')
ylabel('z_2(t)')
xlabel('t (s)')
axis([0 1 -20 20])
hold on

subplot(2,2,1)
plot(t(1),x1(1),'ro',t,x1,'r')
ylabel('x_1(t)')
xlabel('t (s)')
axis([0 1 -20 20])
hold on
subplot(2,2,3)
plot(t(1),x2(1),'ro',t,x2,'r')
ylabel('x_2(t)')
xlabel('t (s)')
axis([0 1 -20 20])
hold on

end