Machine Learning, Dimensionality Reduction, Eigenvectors, Algorithms, Mathematics.
Here’s a video that gives a great explanation if you’re interested in the mathematics - https://www.youtube.com/watch?v=wTsNguVCwrk Essentially, the maxima/minima occur when the gradient of the variance function wrt v and the gradient of the unit sphere generative function wrt v are collinear. i.e