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
收藏
页码：226 / 234
页数：9
相关论文
共 50 条
  • [1] INVERSE M-MATRIX PROBLEM
    WILLOUGHBY, RA
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1977, 18 (01) : 75 - 94
  • [2] The M-matrix group inverse problem for distance-biregular graphs
    Abiad, Aida
    Carmona, Angeles
    Encinas, Andres M.
    Jimenez, Maria Jose
    COMPUTATIONAL & APPLIED MATHEMATICS, 2023, 42 (04):
  • [3] M-matrix and inverse M-matrix extensions
    McDonald, J. J.
    Nandi, R.
    Sivakumar, K. C.
    Sushmitha, P.
    Tsatsomeros, M. J.
    Wendler, Enzo
    Wendler, Megan
    SPECIAL MATRICES, 2020, 8 (01): : 186 - 203
  • [4] On the inverse mean first passage matrix problem and the inverse M-matrix problem
    Neumann, Michael
    Sze, Nung-Sing
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (07) : 1620 - 1630
  • [5] The M-matrix group inverse problem for distance-biregular graphs
    Aida Abiad
    Ángeles Carmona
    Andrés M. Encinas
    María José Jiménez
    Computational and Applied Mathematics, 2023, 42
  • [6] The symmetric inverse M-matrix completion problem
    Johnson, CR
    Smith, RL
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 290 (1-3) : 193 - 212
  • [7] THE SCHUR COMPLEMENT AND THE INVERSE M-MATRIX PROBLEM
    IMAM, IN
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1984, 62 (NOV) : 235 - 240
  • [8] The symmetrical inverse M-matrix completion problem
    He, Ming
    PROCEEDINGS OF THE 14TH CONFERENCE OF INTERNATIONAL LINEAR ALGEBRA SOCIETY, 2007, : 66 - 70
  • [9] INVERSE M-MATRIX INEQUALITIES AND GENERALIZED ULTRAMETRIC MATRICES
    MCDONALD, JJ
    NEUMANN, M
    SCHNEIDER, H
    TSATSOMEROS, MJ
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 220 : 321 - 341
  • [10] Inverse M-matrix completion problem with zeros in the inverse completion
    Jordán, C
    Torregrosa, JR
    Urbano, AM
    APPLIED MATHEMATICS LETTERS, 2002, 15 (06) : 677 - 684
12345