Eigenvectors from eigenvalues
For those curious about applications:Suppose you have a learning algorithm that requires the eigenvectors/eigenvalues for a large matrix. Suppose new data is streamed in that increase the size of the matrix. well, now you have an algorithm for updating your existing solution instead of needing to compute the entire thing from scratch. (consider updating principal components over time for example).Suppose you want to accelerate the process of computing eigenvectors for a large matrix. Well, you can now do parallel reduction relatively trivially given the theorem.*edit: wording.