Principal angles and approximation for quaternionic projections
Operator Algebras
2014-06-13 v1
Abstract
We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in M_n(A) for A the real, complex or quaternionic field (or skew field). From this we derive an algorithm to turn almost commuting projections into commuting projections that minimizes the sum of the displacements of the two projections. We quickly prove what we need using the universal real C*-algebra generated by two projections.
Keywords
Cite
@article{arxiv.1306.1923,
title = {Principal angles and approximation for quaternionic projections},
author = {Terry A. Loring},
journal= {arXiv preprint arXiv:1306.1923},
year = {2014}
}
Comments
11 pages, 4 figures, 4 auxiliary Matlab files