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.
Recommended Citation
P. Zhu and A. V. Knyazev, "Angles between Subspaces and their Tangents," Journal of Numerical Mathematics, vol. 21, no. 4, pp. 325 - 340, De Gruyter, Dec 2013.
The definitive version is available at https://doi.org/10.1515/jnum-2013-0013
Department(s)
Computer Science
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.
Publication Date
01 Dec 2013
Comments
This material is based upon work partially supported by the National Science Foundation under Grant No. 1115734.