On angles, projections and iterations
arXiv:2004.07540 · doi:10.1016/j.laa.2020.05.023
Abstract
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context.
15 pages; published in "Linear Algebra and Its Applications". This version corrects a number of misprints