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Volume 5, Issue 1
Perturbation of Angles Between Linear Subspaces

Ji-Guang Sun

J. Comp. Math., 5 (1987), pp. 58-61.

Published online: 1987-05

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  • Abstract

We consider in this note how the principal angles between column spaces R(A) and R(B) change when the elements in A and B are subject to perturbations. The basic idea in the proof of our results is that the non-zero cosine values of the principal angles between R(A) and R(B) coincide with the non-zero singular values of $P_AP_B$, the product of two orthogonal projections, and consequently we can apply a perturbation theorem of orthogonal projections proved by the author[4].

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@Article{JCM-5-58, author = {Ji-Guang Sun}, title = {Perturbation of Angles Between Linear Subspaces}, journal = {Journal of Computational Mathematics}, year = {1987}, volume = {5}, number = {1}, pages = {58--61}, abstract = {

We consider in this note how the principal angles between column spaces R(A) and R(B) change when the elements in A and B are subject to perturbations. The basic idea in the proof of our results is that the non-zero cosine values of the principal angles between R(A) and R(B) coincide with the non-zero singular values of $P_AP_B$, the product of two orthogonal projections, and consequently we can apply a perturbation theorem of orthogonal projections proved by the author[4].

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9531.html} }
TY - JOUR T1 - Perturbation of Angles Between Linear Subspaces AU - Ji-Guang Sun JO - Journal of Computational Mathematics VL - 1 SP - 58 EP - 61 PY - 1987 DA - 1987/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9531.html KW - AB -

We consider in this note how the principal angles between column spaces R(A) and R(B) change when the elements in A and B are subject to perturbations. The basic idea in the proof of our results is that the non-zero cosine values of the principal angles between R(A) and R(B) coincide with the non-zero singular values of $P_AP_B$, the product of two orthogonal projections, and consequently we can apply a perturbation theorem of orthogonal projections proved by the author[4].

Ji-Guang Sun. (1987). Perturbation of Angles Between Linear Subspaces. Journal of Computational Mathematics. 5 (1). 58-61. doi:
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