Geodesic
Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues
Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 109-132

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DOI

Let $A$ and $B$ be $n\,\times \,n$ complex Hermitian (or real symmetric) matrices with eigenvalues ${{a}_{1}}\,\ge \,\cdots \,\ge \,{{a}_{n}}$ and ${{b}_{1}}\,\ge \,\cdots \,\ge \,{{b}_{n}}$ . All possible inertia values, ranks, and multiple eigenvalues of $A\,+\,B$ are determined. Extension of the results to the sum of $k$ matrices with $k\,>\,2$ and connections of the results to other subjects such as algebraic combinatorics are also discussed.
DOI : 10.4153/CJM-2010-007-2
Mots-clés : complex Hermitian matrices, real symmetric matrices, inertia, rank, multiple eigenvalues 
Li, Chi-Kwong; Poon, Yiu-Tung. Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues. Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 109-132. doi: 10.4153/CJM-2010-007-2
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     journal = {Canadian journal of mathematics},
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