Where I can find necessary and sufficient conditions on eigenvalues of Hermitian matrices with the relation $$A\_1 + A\_2 + ... + A\_n = A\_0 ,$$
i.e. Horn's inequalities for n matrices? 


Can such inequalities be obtained just from Horn's inequalities for 3 matrices if we couple matrices in this way
$$(((A\_1 + A\_2) + A\_3) + A\_4) + ... = A\_0 ?$$


Thanks.



Horn's inequalities for n matrices
1) Section 7 of [Knutson-Tao-Woodward], <http://arxiv.org/pdf/math/0107011.pdf>


2) Yes. To obtain the (minimal set of) inequalities, you can just glom the puzzles together.


