Path product matrices
Path product matrices
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路径乘积矩阵
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
Ronald L. Smith
中科院分区：
文献类型：
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作者：
Charles R. Johnson;Ronald L. Smith
引入了一类新的非负矩阵，称为路径积（PP）矩阵。每个逆M -矩阵都是PP矩阵，这一事实为一些在更广泛背景下成立的关于逆M -矩阵的事实提供了清晰的证明。对于\(n\leq3\)（且不大于3），（严格的）PP矩阵恰好是逆M -矩阵。最后，对PP矩阵进行了研究，给出了一些性质，并解决了部分PP矩阵的完备化问题。与主子矩阵所继承的其他性质不同，部分PP矩阵的可完备性没有图论上的限制。
A new class of nonnegative matrices, called the path product (PP) matrices, is introduced. Every inverse M-matrix is PP and this fact gives transparent proofs of a number of facts about inverse M-matrices that hold in a broader setting. For n≤ 3 (and not greater) the (strict) PP matrices are exactly the inverse M-matrices. Finally, the PP matrices are studied, a number of properties given, and the completion problem is solved for partial PP matrices. Unlike other properties inherited by principal submatrices, there is no graphtheoretic restriction on completability of partial PP matrices.