2 ms·
I think the first point is only true for symmetric matrices (which includes those that show up in multivariable calc). In general, the eigenvectors need not be
by qmalzp 8y ago
I think the first point is only true for symmetric matrices (which includes those that show up in multivariable calc). In general, the eigenvectors need not be orthogonal.
- soVeryTired 8y agoYep, 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 agoIn general it's the eigenvectors of the positive-semidefinite (hence symmetric) part of the left polar decomposition.