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.

引用

页码：309 / 323

页数：15

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