This activity shows the constant surfaces of the function F=xT*M*x. It shows that when the result vector b of Mx=b is placed at the tip of the vector x, that this vector is normal to the constant surfaces of F. When the eigenvectors are both positive or both negative, the function F is an ellipse, and the eigenvectors are oriented along the principle axes of the ellipse (along the principle axes, the normal to the constant surfaces is along the principle axis). When one eigenvector is negtive and the other positive, the function F is a hyperbola. Move the vector x around to see how the transformation behaves (notice that it is consistent with the gradient of F).
