Geodesic
The eigenvalue distribution on Schur complement of nonstrictly diagonally dominant matrices and general $H$-matrices
The electronic journal of linear algebra, Tome 18 (2009), pp. 801-820.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The paper studies the eigenvalue distribution of Schur complements of some special matrices, including nonstrictly diagonally dominant matrices and general H - matrices. Zhang, Xu, and Li [Theorem 4.1, The eigenvalue distribution on Schur complements of H-matrices. Linear Algebra Appl., 422:250-264, 2007] gave a condition for an n$\times n$ diagonally dominant matrix A to have |J R+ (A)| eigenvalues with positive real part and |J R - (A)| eigenvalues with negative real part, where |J R+ (A)| (|J R - (A)|) denotes the number of diagonal entries of A with positive (negative) real part. This condition is applied to establish some results about the eigenvalue distribution for the Schur complements of nonstrictly diagonally dominant matrices and general H - matrices with complex diagonal entries. Several conditions on the n $\times n$ matrix A and the subset $\alpha \subseteq N = {1, 2, \cdot \cdot \cdot , n}$ are
Classification : 15A15, 15A18
Keywords: eigenvalue distribution, Schur complements, (Generalized) diagonally dominant matrices, general H, matrices 
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     title = {The eigenvalue distribution on {Schur} complement of nonstrictly diagonally dominant matrices and general $H$-matrices},
     journal = {The electronic journal of linear algebra},
     pages = {801--820},
     publisher = {mathdoc},
     volume = {18},
     year = {2009},
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Zhang, Cheng-Yi; Luo, Shuanghua; Xu, Fengmin; Xu, Chengxian. The eigenvalue distribution on Schur complement of nonstrictly diagonally dominant matrices and general $H$-matrices. The electronic journal of linear algebra, Tome 18 (2009), pp. 801-820. http://geodesic.mathdoc.fr/item/ELA_2009__18__a0/