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Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues
Abstract Let A and B be n × n complex Hermitian (or real symmetric) matrices with eigenvalues a 1 ≥ … ≥ a n and b 1 ≥ … ≥ b n . All possible inertia values, ranks, and multiple eigenvalues of A + B are determined. Extension of the …