eigen vectors, minimised soln.

Hello,

I just went through a paper for my presentation and stumbled upon some lines which i couldnt resolve yet.

Its a paper on Receptive fields, titled "Slow feature analysis". I have not uploaded the paper here coz i feel my question has no direct relevance to it, for my doubt being mathematical.

In the image shown, they have specified that the eigen vectors of the matrix in equ 8 are the solutions and that they minimise equation 7. That is what i dont understand. I have a medial level of understanding of eigen vectors. But i couldnt resolve as to y it gives the minimised solution.

the numerator in the equation of del is the time derivative of y square (some function) and the denominator is the variance of y. They have to minimise this function becoz, this is a slow feature analysis and so, the derivative of the function under consideration shud be minimal meaning, the slope is minimal and its more or less slow varying function. Most of you wud know this! [:d] but stil....!

thks,
cedance.