Nonsingularity/singularity criteria for nonstrictly block diagonally dominant matrices
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- 作者：Kolotilina ; L.Yu.
- 关键词：15A42 ; Irreducibility ; Nonstrict (block) diagonal dominance ; Nonsingularity ; Gerschgorin circles ; Ovals of Cassini
- 刊名：Linear Algebra and its Applications
- 出版年：2003
- 出版时间：January 15, 2003
- 年：2003
- 卷：359
- 期：1-3
- 页码：133-159
- 全文大小：186 K
文摘
Let A=(Aij)Ni,j=1
Cn×n be a block irreducible matrix with nonsingular diagonal blocks, v=(vi)CN be a positive vector, and let Formula Not Shown Under these assumptions, necessary and sufficient conditions for A to be singular are obtained based on a block generalization of Wielandt’s lemma. The pointwise case (N=n) of irreducible matrices with nonstrict generalized diagonal dominance is treated separately.
Cn×n be a block irreducible matrix with nonsingular diagonal blocks, v=(vi)CN be a positive vector, and let Formula Not Shown Under these assumptions, necessary and sufficient conditions for A to be singular are obtained based on a block generalization of Wielandt’s lemma. The pointwise case (N=n) of irreducible matrices with nonstrict generalized diagonal dominance is treated separately.