四元数投影的顶角与逼近
Principal angles and approximation for quaternionic projections
摘要：
本文将Jordan的顶角概念推广到四元数空间的两个子空间，从而得到了分析实、复或四元数域（或除环）在M_n（A）中的两个正交投影的方法.由此，我们推导出一个算法，把几乎可交换的投影到可交换的投影，最大限度地减少两个投影的位移之和。我们使用由两个投影生成的通用实C* 代数来快速证明我们所需要的。
英文摘要：
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 M_n(A) for A 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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