Sum of Hermitian Matrices with Given Eigenvalues: Inertia, Rank, and Multiple Eigenvalues
Printed: Feb 2010
Let $A$ and $B$ be $n\times n$ complex Hermitian (or real symmetric) matrices
with eigenvalues $a_1 \ge \dots \ge a_n$ and $b_1 \ge \dots \ge b_n$.
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.
complex Hermitian matrices, real symmetric matrices, inertia, rank, multiple eigenvalues
15A42 - Inequalities involving eigenvalues and eigenvectors
15A57 - Other types of matrices (Hermitian, skew-Hermitian, etc.)