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Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.
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There is an observation on the eigenvalues of the sum of a kind of special Hermitian matrice...
Suppose $A$ and $B$ belong to a kind of special hermitian matrices, which have the following properties:
$A$ and $B$ contain only one negative eigenvalue.
the negative eigenvalue and the second-large …