Annals of Functional Analysis

Principal angles and approximation for quaternionic projections

Terry A. Loring

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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.

Article information

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

Dates
First available in Project Euclid: 7 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1396833512

Digital Object Identifier
doi:10.15352/afa/1396833512

Mathematical Reviews number (MathSciNet)
MR3192019

Zentralblatt MATH identifier
1297.15035

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

Keywords
Principal angles subspace projection quaternions

Citation

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


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