Timeline for rank-one perturbation of a matrix corresponding to a specific spectrum

7 events

when toggle format	what		by	license	comment
Apr 26, 2015 at 7:32	history	edited	Ricardo Andrade	CC BY-SA 3.0	replaced tag 'spectral'
Jun 1, 2011 at 8:37	answer	added	Vedarun		timeline score: 0
May 31, 2011 at 18:22	comment	added	Pietro Majer		To clarify, can you confirm: $A'=A+\epsilon H$; $A$ and $H$ are symmetric and $H$ is rank-one, thus $H=u\otimes u$. The second eigenvector of $A'$ is prescribed. It is not necessarily the second eigenvector of $A$, though. Also, it seems implicitly assumed that the second eigenvalue (in decreasing order?) of $A'$ is simple.
May 31, 2011 at 15:44	answer	added	Igor Rivin		timeline score: 2
May 31, 2011 at 15:03	comment	added	Michael Renardy		It is not too hard to characterize rank one perturbations which make a given vector an eigenvector. I assume what makes the problem difficult is to guarantee that this eigenvector is the "second" one. You did not state the criterium for ordering, however.
May 31, 2011 at 7:21	history	edited	Denis Serre	CC BY-SA 3.0	added 11 characters in body
May 31, 2011 at 6:37	history	asked	Vedarun	CC BY-SA 3.0