On p-tuples of the Grassmann manifolds |
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Authors: | Joël Rouyer |
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Institution: | 1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania
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Abstract: | We provide a matrix invariant for isometry classes of p-tuples of points in the Grassmann manifold ${G_{n}\left(\mathbb{K}^{d}\right) }$ ( ${\mathbb{K=\mathbb{R}}}$ or ${\mathbb{C}}$ ). This invariant fully characterizes the p-tuple. We use it to classify the regular p-tuples of ${G_{2}\left(\mathbb{R}^{d}\right) }$ , ${G_{3}\left( \mathbb{R}^{d}\right) }$ and ${G_{2}\left( \mathbb{C}^{d}\right) }$ . |
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