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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.

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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.

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