On Schur complement of block diagonally dominant matrices

• Published in: Linear algebra and its applications Vol. 414; no. 2-3; pp. 533 - 546
• Main Authors: Zhang, Cheng-yi, Li, Yao-tang, Chen, Feng
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.04.2006; Elsevier Science
• Subjects: Algebra; Exact sciences and technology; I-(II-)block diagonally dominant matrices; I-(II-)generalized block diagonally dominant matrices; Linear and multilinear algebra, matrix theory; Mathematics; Schur complements; Sciences and techniques of general use; Schur complements; I-(II-)generalized block diagonally dominant matrices; I-(II-)block diagonally dominant matrices; 15A48; 15A45; Linear algebra; Dominance; 15A48 Schur complements; Schur complement; Generalized; Block matrix
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/j.laa.2005.10.046

It is well-known that the Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant [D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251]; the same is true of generalized strictly diagonally dominant matrices [Jianzhou Liu, Yungqing Huang, Some properties on Schur complements of H-matrix and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365–380]. In this paper, this result is extended to the block (strictly) diagonally dominant matrices and the generalized block (strictly) diagonally dominant matrices, that is, it is shown that the Schur complement of a block (strictly) diagonally dominant matrix is a block (strictly) diagonally dominant matrix and so is the Schur complement of a generalized block (strictly) diagonally dominant matrix.