Title

Angles between Subspaces and their Tangents

Abstract

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and non-orthonormal bases for subspaces, as well as projectors. Such a construction has applications, e.g., in analysis of convergence of subspace iterations for eigenvalue problems.

Department(s)

Computer Science

Comments

This material is based upon work partially supported by the National Science Foundation under Grant No. 1115734.

Keywords and Phrases

Canonical angles; Eigenvalue problem; Orthonormal; Principal angles; Projector; Singular values; Subspace iterations; Computational methods; Mathematical techniques; Eigenvalues and eigenfunctions

International Standard Serial Number (ISSN)

1570-2820; 1569-3953

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2013 De Gruyter, All rights reserved.

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