Terry A. Loring

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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.


The Matlab files stored here were used to create the test data in "Principal angles and approximation for quaternionic projections" which is expected to be published, pending minor revision, by Annals of Functional Analysis, in a special volume dedicated to Professor Tsuyoshi Ando. These files run under Matlab R2103b. The files here are: testAngle.m testCommute.m fixCommute.m spectral.m Readers are invited to examine and run testAngle() to validate the algorithm described in Section 2.2, that computes principal vectors. All three figures in the paper were created using testCommute(200,100).