Perturbation of Angles Between Linear Subspaces (Journal of Computational Mathematics, 1987)
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].