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

Li, Chi-Kwong
; 
Poon, Yiu-Tung
Abstract
Let A and B be n x 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 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.
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2010-01-01
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Mathematics
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Mathematics
DOI
10.4153/CJM-2010-007-2
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https://scholarworks.wm.edu/handle/internal/536
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