A converse of a matrix inequality

被引：1
|
作者：
Alzer, H
机构：
[1] Morsbacher Strasse 10
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2001年 / 323卷 / 1-3期
关键词：
matrix inequality; Cauchy's inequality;
D O I：
10.1016/S0024-3795(00)00259-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove: if (x(ij)) is an m x n matrix with non-negative real entries, which are not all equal to 0, then [GRAPHICS] with the best possible lower bound [GRAPHICS] Our theorem complements a result of E.R. van Dam [Linear Algebra Appl. 280 (1998) 163], who established that in the case of real entries the best possible upper bound is equal to 1, (C) 2001 Elsevier Science Inc. All rights reserved. AMS classification: 15A45; 26D15.
引用
收藏
页码：195 / 199
页数：5
相关论文
共 50 条
  • [11] ON A CONVERSE OF KY FAN INEQUALITY
    Simic, Slavko
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2010, 33 : 95 - 99
  • [12] GENERALIZATION OF A CONVERSE OF HOLDERS INEQUALITY
    LEINDLER, L
    ACTA SCIENTIARUM MATHEMATICARUM, 1976, 38 (1-2): : 107 - 112
  • [13] Converse Jensen–Steffensen inequality
    S. Ivelić
    M. Klaričić Bakula
    J. Pečarić
    Aequationes mathematicae, 2011, 82 : 233 - 246
  • [14] A CONVERSE TO VON NEUMANN INEQUALITY
    ROVNYAK, J
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 84 (03) : 370 - 372
  • [15] CONVERSE TO THE SHERMAN INEQUALITY WITH APPLICATIONS
    Barbir, Ana
    Bradanovic, Slavica Ivelic
    Pecaric, Dilda
    Pecaric, Josip
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (04): : 1405 - 1419
  • [16] Converse theorem for the Minkowski inequality
    Matkowski, Janusz
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (01) : 315 - 323
  • [17] A CONVERSE OF THE HOLDER INEQUALITY THEOREM
    Matkowski, Janusz
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2009, 12 (01): : 21 - 32
  • [18] The inequality of Milne and its converse
    Alzer, H
    Kovacec, A
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2002, 7 (04) : 603 - 611
  • [19] A converse of Minkowski's inequality
    Alzer, H
    Ruscheweyh, S
    DISCRETE MATHEMATICS, 2000, 216 (1-3) : 253 - 256
  • [20] A converse to Cauchy's inequality
    Zagier, D
    AMERICAN MATHEMATICAL MONTHLY, 1995, 102 (10): : 919 - 926
12345