Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices. (English) Zbl 1133.15020

The authors prove that the diagonal-Schur complement of a strictly doubly diagonally dominant matrix is a strictly generalized doubly diagonally dominant matrix. They provide the distribution of the real parts of eigenvalues of a diagonal-Schur complement of an \(H\)-matrix. They obtain a sufficient condition to ensure that the Schur complement of an \(r\)-diagonally dominant matrix is \(r\)-diagonally dominant.


15B57 Hermitian, skew-Hermitian, and related matrices
15B48 Positive matrices and their generalizations; cones of matrices
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