3 ms·

Yep, you could well be right. The image of an ellipse under a linear transform is definitely an ellipse, but I'm not sure about the eigenvectors in the general

Yep, you could well be right. The image of an ellipse under a linear transform is definitely an ellipse, but I'm not sure about the eigenvectors in the general case. The symmetric case is by far the most relevant for probability theory though.

tprice7 8y ago
In general it's the eigenvectors of the positive-semidefinite (hence symmetric) part of the left polar decomposition.