Principal Angles and Approximation for Quaternionic Projections

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 the matrices over 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. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA. E-mail address: [email protected] Date: Received: June 8, 2013; Accepted: December 13, 2013. 2010 Mathematics Subject Classification. Primary 15B33; Secondary 46L05.