Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues

Abstract

AbstractLet A and B be n × n complex Hermitian (or real symmetric) matrices with eigenvalues a1 ≥ … ≥ an and b1 ≥ … ≥ bn. 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.