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2014 Principal angles and approximation for quaternionic projections
Terry A. Loring
Ann. Funct. Anal. 5(2): 176-187 (2014). DOI: 10.15352/afa/1396833512

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 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.

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Terry A. Loring. "Principal angles and approximation for quaternionic projections." Ann. Funct. Anal. 5 (2) 176 - 187, 2014. https://doi.org/10.15352/afa/1396833512

Information

Published: 2014
First available in Project Euclid: 7 April 2014

zbMATH: 1297.15035
MathSciNet: MR3192019
Digital Object Identifier: 10.15352/afa/1396833512

Subjects:
Primary: 15B33
Secondary: 46L05

Rights: Copyright © 2014 Tusi Mathematical Research Group

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Vol.5 • No. 2 • 2014
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