English

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

R2 v1 2026-06-22T00:30:24.783Z