两个子空间之间的几何特征

数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 879-891.

两个子空间之间的几何特征

杜鸿科¹|高桂宝^1,2|王月清³

1.陕西师范大学数学与信息科学学院西安 |710062|2.运城学院应用数学系山西运城 044000|3.重庆科技学院重庆 |400042

收稿日期:2010-06-20 修回日期:2012-01-08 出版日期:2012-10-25 发布日期:2012-10-25
基金资助:
国家自然科学基金(10571113)资助

Geometry Characterizations Between Two Subspaces

DU Hong-Ke¹, GAO Gui-Bao^1,2, WANG Rue-Qing³

1.College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062; 2.Applied Mathematics Department,Yuncheng University, Shanxi |Yuncheng 044000; 3.Chongqing University of Science and Technology, Chongqing 401331

Received:2010-06-20 Revised:2012-01-08 Online:2012-10-25 Published:2012-10-25
Supported by:
国家自然科学基金(10571113)资助

摘要/Abstract

摘要：

对希尔伯特空间中的有界线性算子运用分块算子矩阵技巧, 讨论了两个子空间的几何结构, 得到了两个子空间的距离和夹角的新的特征, 给出了两个子空间的Kovarik公式的表示. 改进了文献[11]给出的两个定理.

关键词: 子空间, 正交投影, Kovarik 公式, 组合逼近

Abstract:

By using the technique of block-operator matrices of bounded linear operators on a Hilbert space, in this paper, the geometry structure between two subspaces are investigated. New characterizations of the distance and the angle between two subspaces are established. The representation of Kovarik formula of two subspaces are obtained. The alternative proofs of two theorems concerning combination approximations (M. Hegland, J. Garcke, V. Challis, The combination technique and some generalizations, Linear Algebra and its Applications, to appear) are given.

Key words: Subspace, Orthogonal projection, Kovarik formula, Combination approximation

中图分类号:

47A05

杜鸿科, 高桂宝, 王月清. 两个子空间之间的几何特征[J]. 数学物理学报, 2012, 32(5): 879-891.

DU Hong-Ke, GAO Gui-Bao, WANG Rue-Qing. Geometry Characterizations Between Two Subspaces[J]. Acta mathematica scientia,Series A, 2012, 32(5): 879-891.

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