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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? enter image description here

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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.

Also have a look at this.

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