Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (5): 879-891.

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Geometry Characterizations Between Two Subspaces

 DU Hong-Ke1, GAO Gui-Bao1,2, WANG Rue-Qing3   

  1. 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

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

CLC Number: 

  • 47A05
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