IMPROVED TESTS AND CHARACTERIZATIONS OF TOTALLY NONNEGATIVE MATRICES

被引：11
作者：
Adm, Mohammad [1 ,2 ]
Garloff, Juergen [3 ]
机构：
[1] Univ Konstanz, Dept Math & Stat, D-78464 Constance, Germany
[2] Palestine Polytech Univ, Dept Math, Hebron, Israel
[3] Univ Appl Sci HTWG Konstanz, Fac Comp Sci, D-78405 Constance, Germany
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2014年 / 27卷
关键词：
Totally nonnegative matrix; Totally positive matrix; Cauchon algorithm; Neville elimination; Bidiagonalization; POSITIVE MATRICES; NEVILLE ELIMINATION; CELLS;
D O I：
10.13001/1081-3810.1920
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are considered. A condensed form of the Cauchon algorithm which has been proposed for finding a param-eterization of the set of these matrices with a fixed pattern of vanishing minors is derived. The close connection of this variant to Neville elimination and bidiagonalization is shown and new determinantal tests for total nonnegativity are developed which require much fewer minors to be checked than for the tests known so far. New characterizations of some subclasses of the totally nonnegative matrices as well as shorter proofs for some classes of matrices for being (nonsingular and) totally nonnegative are derived.
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收藏
页码：588 / 610
页数：23
相关论文
共 18 条
  • [11] Pentadiagonal oscillatory matrices with two spectrum in common
    Ghanbari, Kazem
    [J]. POSITIVITY, 2006, 10 (04) : 721 - 729
  • [12] Inner totally positive matrices
    Gladwell, GML
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 393 : 179 - 195
  • [13] Gladwell GML, 1998, LINEAR ALGEBRA APPL, V271, P257
  • [14] Totally nonnegative cells and matrix Poisson varieties
    Goodearl, K. R.
    Launois, S.
    Lenagan, T. H.
    [J]. ADVANCES IN MATHEMATICS, 2011, 226 (01) : 779 - 826
  • [15] Total nonpositivity of nonsingular matrices
    Huang, Rong
    Chu, Delin
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (11) : 2931 - 2941
  • [16] Efficient Recognition of Totally Nonnegative Matrix Cells
    Launois, S.
    Lenagan, T.
    [J]. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2014, 14 (02) : 371 - 387
  • [17] Pinkus A., 2010, CAMBRIDGE TRACTS MAT, V181
  • [18] Whitney A., 1952, Journal d'Analyse Mathematique, V2, P88
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