Geodesic
Schur complements of generally diagonally dominant matrices and a criterion for irreducibility of matrices
The electronic journal of linear algebra, Tome 18 (2009), pp. 69-87.

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

Summary: As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H - matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset $\alpha \subset {1, 2, . . . , n}$ so that the Schur complement matrix $A/\alpha $is an H - matrix. These conditions are then applied to decide whether a matrix is irreducible or not.
Classification : 15A15, 15F10
Keywords: Schur complement, diagonally dominant matrices, H, matrices, irreducible, re- ducible 
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     title = {Schur complements of generally diagonally dominant matrices and a criterion for irreducibility of matrices},
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Zhang, Cheng-Yi; Luo, Shuanghua; Xu, Chengxian; Jiang, Hongying. Schur complements of generally diagonally dominant matrices and a criterion for irreducibility of matrices. The electronic journal of linear algebra, Tome 18 (2009), pp. 69-87. http://geodesic.mathdoc.fr/item/ELA_2009__18__a51/