publication . Article . Other literature type . 1973

Numerical Methods for Computing Angles Between Linear Subspaces

Bjorck, Ake; Golub, Gene H.;
Restricted
  • Published: 01 Sep 1973 Journal: Mathematics of Computation, volume 27, page 579 (issn: 0025-5718, Copyright policy)
  • Publisher: JSTOR
Abstract
Assume that two subspaces F and G of unitary space are defined as the ranges (or nullspaces) of given rectangular matrices A and B. Accurate numerical methods are developed for computing the principal angles $\theta_k (F,G)$ and orthogonal sets of principal vectors $u_k\ \epsilon\ F$ and $v_k\ \epsilon\ G$, k = 1,2,..., q = dim(G) $\leq$ dim(F). An important application in statistics is computing the canonical correlations $\sigma_k\ = cos \theta_k$ between two sets of variates. A perturbation analysis shows that the condition number for $\theta_k$ essentially is max($\kappa (A),\kappa (B)$), where $\kappa$ denotes the condition number of a matrix. The algorithm...
Subjects
free text keywords: Algebra and Number Theory, Applied Mathematics, Computational Mathematics, Numerical analysis, Least squares, Singular value, Discrete mathematics, Linear subspace, Combinatorics, Matrix (mathematics), Perturbation theory, Condition number, Numerical linear algebra, computer.software_genre, computer, Mathematics
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publication . Article . Other literature type . 1973

Numerical Methods for Computing Angles Between Linear Subspaces

Bjorck, Ake; Golub, Gene H.;