Take the 2-minute tour ×  Is there a relationship between the
eigenvalues of individual matrices and the eigenvalues of their
sum?  What about the special case when they are Hermitian and
positive-definite?  I am investigating this with regard to
finding the normalized graph cut under general convex
constraints.  Any pointers will be very helpful.  Thanks. B.
share|improve this question  4 Answers 4  up vote 30 down vote
accepted  The problem of describing the possible eigenvalues of
the sum of two hermitian matrices in terms of the spectra of the
summands leads into deep waters. The most complete description
was conjectured by Horn, and has now been proved by work of
Knutson and Tao (and others?) - for a good discussion, see the
Notices AMS article by those two authors  Depending on what you
want, there should be simpler results giving estimates on the
eigenvalues of the sum. A book like Bhatia's Matrix Analysis
might have some helpful material.  share|improve this answer  A
simple estimate which is often u