The geometrical meaning of the Kantorovich-Wielandt inequalities

被引：14
|
作者：
Gustafson, K [1 ]
机构：
[1] Univ Colorado, Dept Math, Boulder, CO 80309 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 1999年 / 296卷 / 1-3期
关键词：
operator trigonometry; Kantorovich-Wielandt; anti-eigenvector;
D O I：
10.1016/S0024-3795(99)00106-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Kantorovich-Wielandt angle theta(A) and the author's operator angle phi(A) are related by cos phi(A(2)) = sin theta(A). Here A is an arbitrary symmetric positive definite (SPD) matrix. The relationship of these two different geometrical perspectives is discussed. An extension to arbitrary nonsingular matrices A is given. A related four-way relationship with the operator trigonometry, strengthened CBS constants, and domain decomposition methods is noted. (C) 1999 Elsevier Science Inc. All rights reserved.
引用
收藏
页码：143 / 151
页数：9
相关论文
共 50 条
  • [31] The geometrical meaning of time
    Yahalom, Asher
    FOUNDATIONS OF PHYSICS, 2008, 38 (06) : 489 - 497
  • [32] The Geometrical Meaning of Time
    Asher Yahalom
    Foundations of Physics, 2008, 38 : 489 - 497
  • [33] On the Davis-Wielandt radius inequalities of Hilbert space Operators
    Alomari, M. W.
    LINEAR & MULTILINEAR ALGEBRA, 2023, 71 (11): : 1804 - 1828
  • [34] Kantorovich type reverse inequalities for operator norm
    Fujii, JI
    Seo, Y
    Tominaga, M
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2005, 8 (03): : 529 - 535
  • [35] Several matrix Kantorovich-type inequalities
    Liu, SZ
    Neudecker, H
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 197 (01) : 23 - 26
  • [36] NEW KANTOROVICH TYPE INEQUALITIES FOR NEGATIVE PARAMETERS
    Furuichi, S.
    Moradi, H. R.
    ANALYSIS MATHEMATICA, 2020, 46 (04) : 747 - 760
  • [37] KANTOROVICH TYPE OPERATOR INEQUALITIES FOR FURUTA INEQUALITY
    Seo, Yuki
    OPERATORS AND MATRICES, 2007, 1 (01): : 143 - 152
  • [38] IMPROVED YOUNG AND HEINZ INEQUALITIES WITH THE KANTOROVICH CONSTANT
    Liao, Wenshi
    Wu, Junliang
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (02): : 559 - 570
  • [39] Several Generalized Matrix Versions of Kantorovich Inequalities
    李树有
    张宝学
    李馨
    NortheasternMathematicalJournal, 2003, (04) : 346 - 350
  • [40] On Some Matrix Kantorovich-Type Inequalities
    He, Gan-tong
    PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPPLICATIONS, VOL 1, 2009, : 217 - 220
12345