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A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.
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篇名 Non-Singularity Conditions for Two Z-Matrix Types
来源期刊 线性代数与矩阵理论研究进展(英文) 学科 数学
关键词 Z-MATRIX M-MATRIX Non-Negative Matrix DIAGONAL DOMINANCE
年,卷(期) 2014,(2) 所属期刊栏目
研究方向 页码范围 109-119
页数 11页 分类号 O1
字数 语种
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Z-MATRIX
M-MATRIX
Non-Negative
Matrix
DIAGONAL
DOMINANCE
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线性代数与矩阵理论研究进展(英文)
季刊
2165-333X
武汉市江夏区汤逊湖北路38号光谷总部空间
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93
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0
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