Document Zbl 1297.15035

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Principal angles and approximation for quaternionic projections. (English) Zbl 1297.15035

Ann. Funct. Anal. 5, No. 2, 176-187 (2014).

Summary: 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.

Cited in 2 Documents

MSC:

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

Keywords:

principal angles; subspace; projection; quaternions; algorithm; \(C^*\)-algebra

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