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3 votes

Optimizing directly on the eigenspectrum of a matrix

Many (but not all) problems involving the eigenvalues of a graph are convex optimization problems that can be formulated as semidefinite programming problems. There are a number of "tricks" that you …
Brian Borchers's user avatar
1 vote

Norm bound on eigen-vector change caused by rank-one update

A tiny change can result in a shift of the dominant eigenvalue's eigenspace to something that is completely orthogonal to the dominant eigenvalue's eigenspace of $A$. For example, let $A=I-\epsil …
Brian Borchers's user avatar