The many proofs of an identity on the norm of oblique projections

被引：92
|
作者：
Szyld, Daniel B. [1 ]
机构：
[1] Temple Univ, Dept Math, Philadelphia, PA 19122 USA
来源：
NUMERICAL ALGORITHMS | 2006年 / 42卷 / 3-4期
关键词：
idempotent operators; oblique projections; angle between subspaces; gap between subspaces;
D O I：
10.1007/s11075-006-9046-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P-2 = P, which is neither null nor the identity, it holds that parallel to P parallel to = parallel to I - P parallel to. This useful equality, while not widely-known, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler ones are presented.
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页码：309 / 323
页数：15
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