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
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