13 November, 2019 at 1:52 pm Anonymous
Why do you say that eigenvectors are determined by eigenvalues? For example, for symmetric matrices you still do not know n-squared plus or minus signs of the coordinates. Isn’t finding the signs almost as hard to finding eigenvectors themselves? 13 November, 2019 at 4:32 pm Terence Tao The title is indeed an oversimplification (it seemed to convey the essence of the result more succinctly than “norm square of coefficients of eigenvectors from eigenvalues”). The second sentence of the abstract is intended to clarify the sense in which we relate eigenvectors and eigenvalues. On Fri, Nov 15, 2019 at 1:43 PM Roger Hui <[email protected]> wrote: > The theorem gives information on the square of every element (component) of > every eigenvector. That's a lot of information and that's consistent with > the informal description "compute eigenvectors using only information about > eigenvalues". > > > On Fri, Nov 15, 2019 at 9:58 AM Raul Miller <[email protected]> wrote: > > > On Fri, Nov 15, 2019 at 11:22 AM Roger Hui <[email protected]> > > wrote: > > > The actual theorem and proofs: > > > https://terrytao.wordpress.com/tag/xining-zhang/ > > > > I am only seeing a calculation for the magnitudes of the eigenvectors, > > there. > > > > (Am I missing something obvious?) > > > > Thanks, > > > > -- > > Raul > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
