Principal Angles Between Subspaces and Their Tangents

    •  Zhu, P.; Knyazev, A., "Principal angles between subspaces and their tangents," Tech. Rep. TR2012-058, arXiv, September 2012.
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      • @techreport{Zhu2012sep,
      • author = {Zhu, P. and Knyazev, A.},
      • title = {Principal angles between subspaces and their tangents},
      • journal = {arXiv},
      • year = 2012,
      • month = sep,
      • url = {}
      • }

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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 and used via their cosines. The tangents of PABS have attracted relatively less attention, but are important for analysis of convergence of subspace iterations for eigenvalue problems. We explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and nonorthonormal bases for subspaces, and orthogonal projectors.