Principal Angles between Subspaces in an A-Based Scalar Product: Algorithms and Perturbation Estimates

An Effective and Robust Algorithm for Finding Principal Angles between Subspaces Using an A-based Scalar Product

Canonical angles and limits of sequences of EP and co-EP matrices

Let A be a square complex matrix. Let P be one of the following properties: (a) A is an EP matrix, (b) the column space of A is complementary to the column space of A Ã , and (c) the orthogonal complement of the column space of A is the column space of A Ã. We study the canonical angles between the column space of A and the column space of A Ã when A satisfies property P. Also, we research the ...

Majorization : Angles , Ritz Values

Many inequality relations between real vector quantities can be succinctly expressed as “weak (sub)majorization” relations using the symbol ≺w. We explain these ideas and apply them in several areas: angles between subspaces, Ritz values, and graph Laplacian spectra, which we show are all surprisingly related. Let Θ(X ,Y) be the vector of principal angles in nondecreasing order between subspace...

New Estimates of the Spectral Dichotomy

We derive new estimates of the spectral dichotomy for matrices and matrix pencils which are based upon estimates of the restrictions of Green functions associated with the spectrum dichotomy problem onto the stable and unstable invariant subspaces and estimates of angles between these subspaces. De nouvelles estimations pour la dichotomie spectrale R esum e : Nous etablissons de nouvelles estim...

Boosted manifold principal angles for image set-based recognition

In this paper we address the problem of classifying vector sets. We motivate and introduce a novel method based on comparisons between corresponding vector subspaces. In particular, there are two main areas of novelty: (i) we extend the concept of principal angles between linear subspaces to manifolds with arbitrary nonlinearities; (ii) it is demonstrated how boosting can be used for applicatio...