The M-matrix group generalized inverse problem for weighted trees

被引：14

作者：

Kirkland, SJ ^{[1
]}

Neumann, M

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1998年 / 19卷 / 01期

关键词：

Laplacian matrix; impedance matrix; weighted tree;

D O I：

10.1137/S0895479896304927

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize all weighted trees whose Laplacian has a group inverse which is an M matrix. Actually, only a very narrow set of weighted trees yields such Laplacians. Our investigation involves analyzing circumstances under which a certain Z-matrix, derived from the tree and whose order is one less than the number of vertices in the tree, is an M-matrix. Our work here is motivated by a recent paper of Styan and Subak-Sharpe [Linear Algebra Appl., 250 (1997), pp. 349-370] and by an earlier question of Deutsch and Neumann [J. Math. Anal. Appl., 102 (1984), pp. 1-29].

引用

页码：226 / 234

页数：9

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