# How to understand relationships between ellipse and second moment matrix of Harris corner detector?

guys. I am really lacking in knowledge of linear algebra. I am reading slides of Harris corner. But I am really confused about one of them. I know that I can find corners by two large eigenvalues but I can not consider it as an ellipse....can anybody give me any suggestions?

Consider a 2-by-2 diagonal matrix $M$ with diagonal elements $a>0$ and $b>0$. Then the equation
$$x^TMx=const\tag{1}$$
(with $x$ a column vector with elements $u$ and $v$) becomes
$$au^2 + bv^2 = const$$
which is simply the equation of an ellipse (or a circle if $a=b$). If $M$ is not diagonal, equation (1) still describes an ellipse if $M$ is positive definite (i.e. it has positive eigenvalues), but then its major and minor axes do not coincide with the Cartesian axes.