How to understand relationships between ellipse and second moment matrix of Harris corner detector?
Consider a 2-by-2 diagonal matrix $M$ with diagonal elements $a&gt;0$ and $b&gt;0$. 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.

Also have a look at this.