Annals of Functional Analysis

Principal angles and approximation for quaternionic projections

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.

Article information

Ann. Funct. Anal., Volume 5, Number 2 (2014), 176-187.

First available in Project Euclid: 7 April 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15B33: Matrices over special rings (quaternions, finite fields, etc.)
Secondary: 46L05: General theory of $C^*$-algebras

Principal angles subspace projection quaternions


Loring, Terry A. Principal angles and approximation for quaternionic projections. Ann. Funct. Anal. 5 (2014), no. 2, 176--187. doi:10.15352/afa/1396833512.

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