cd

v:\cursos\pos\otimiza\aulas

H=rand(3)

H =

    0.4447    0.9218    0.4057
    0.6154    0.7382    0.9355
    0.7919    0.1763    0.9169

H=1/2*(H+H');
H

H =

    0.4447    0.7686    0.5988
    0.7686    0.7382    0.5559
    0.5988    0.5559    0.9169

[V,L]=eig(H)

V =

    0.8083   -0.2557    0.5303
   -0.5696   -0.5676    0.5945
   -0.1489    0.7826    0.6045


L =

   -0.2072         0         0
         0    0.3181         0
         0         0    1.9890

V(:,1)'*V(:,2)

ans =

 -2.7756e-017

V(:,1)'*V(:,3)

ans =

  1.6653e-016

inv(V)

ans =

    0.8083   -0.5696   -0.1489
   -0.2557   -0.5676    0.7826
    0.5303    0.5945    0.6045

V'

ans =

    0.8083   -0.5696   -0.1489
   -0.2557   -0.5676    0.7826
    0.5303    0.5945    0.6045

L

L =

   -0.2072         0         0
         0    0.3181         0
         0         0    1.9890

H

H =

    0.4447    0.7686    0.5988
    0.7686    0.7382    0.5559
    0.5988    0.5559    0.9169


M1=H(1,1)

M1 =

    0.4447

M2=H(1:2,1:2)

M2 =

    0.4447    0.7686
    0.7686    0.7382

M3=H

M3 =

    0.4447    0.7686    0.5988
    0.7686    0.7382    0.5559
    0.5988    0.5559    0.9169


det(M1)

ans =

    0.4447

det(M2)

ans =

   -0.2625

det(M3)

ans =

   -0.1311

cd

v:\cursos\pos\otimiza\aulas

type semidef

x1=[-5:.5:5]';
x2=x1;
[X1,X2]=meshgrid(x1,x2);
s=X1.^2+X1.*(X2.^2);
mesh(X1,X2,s); figure(gcf);
xlabel('x1'); ylabel('x2'); zlabel('S(x)');
% cinvert

semidef
diary off