Angles between subspaces and their tangents

By Peizhen Zhu, Andrew V. Knyazev. 2012

92 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

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In Computational Theory and Mathematics

1. Pierre Alquier
2. Thang Van Doan

Citations in the corpus

• A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix (2020, background): “…and τ T represented by their orthonormal basis concatenated respectively in V τ S and V τ T , the elements of the diagonal matrix Θ τ S → τ T resulting from the SVD decomposition of V τ S V τ T are the cosines of the principal angles between these two subspace [Wedin, 1983, Zhu and Knyazev, 2013].”