Angles between Subspaces and their Tangents
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.
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
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)
Article - Journal
© 2013 De Gruyter, All rights reserved.
01 Dec 2013