% 3D visualization of x'Ax written by kihwan choi
% A is a symmetric matrix in R^3
clear all;
close all;
randn('state', 1);
A = randn(3); % generate a random matrix in R^3
A = (A+A')/2; % update A with the symmertic part of A

% generate a sphere with n-by-n faces
n = 100; % larger n higher resolution
[X Y Z] = sphere(n); 

% assign x'Ax as the color value
for i = 1:n+1
   for j = 1:n+1
      C(i,j) = [X(i,j);Y(i,j);Z(i,j)]'*A*[X(i,j);Y(i,j);Z(i,j)];
   end
end

% plot the result
surf(X,Y,Z,C,'Edgecolor','none');
axis square;