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.
Keywords
Cite
@article{arxiv.1209.0523,
title = {Angles between subspaces and their tangents},
author = {Peizhen Zhu and Andrew V. Knyazev},
journal= {arXiv preprint arXiv:1209.0523},
year = {2016}
}
Comments
15 pages, 1 figure, 2 tables. Accepted to Journal of Numerical Mathematics