A=load('lena512.mat');%load the picture
%in Matlab this returns a struct variable
A=A.lena512;%we only need the matrix field, so we can simply overwrite the A variable

%now A is matrix containing numbers from 0 to 255
%to get a greyscale image, we can use 
%colormap command, which takes as its argument 
%a matrix that determines RGB components for indexed colors
scale=linspace(0,1,255);
colormap([scale;scale;scale]');
figure(1);
image(A);%produce the image

[U,S,V]=svd(A);%the svd decompostion
%the matrix S contains the singular values on the diagonal in descending order 
s=diag(S);%extracting the diagonal into a column vector

for n=[10 20 50 100]%for selected values of n
    figure(n);
    An=U(:,1:n)*S(1:n,1:n)*V(:,1:n)';%we form an approximation
    %of A using only the n largest singular values
    image(round(An));
end