% Read in the image build a symmetric image
load clown
figure(1)
image(X)
colormap(map)
axis square
X=X';
%Force it to be purely symmetric
A=zeros(200,200);
for j=1:200
    temp=X(j:200,j);
    A(j:end,j)=temp;
    A(j,j:end)=temp';
end
figure(2)
image(A)
colormap(map)
axis square

%Find the eigenvalues (in matrix D) and eigenvecs (in V).
[V,D]=eig(A);

%Plot the spectral decomposition, ordered by the magnitude of the
%eigenvalues:
t=diag(D);
[val,idx]=sort(abs(t),'descend');

figure(3)
image(A)
colormap(map)
axis square

for j=1:60
    H=V(:,idx(1:j))*diag(t(idx(1:j)))*V(:,idx(1:j))';
    image(round(H))
    Err(j)=norm(H-A,'fro');
    pause(0.1)
end