Plücker coordinates: Difference between revisions
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m →Projective distance: Typo R^n |
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In Euclidean space, one usually takes advantage of the dot product to measure angles. | In Euclidean space, one usually takes advantage of the dot product to measure angles. | ||
Given vectors <math>a, b \in \mathbb{R^n | Given vectors <math>a, b \in \mathbb{R}^n</math>, we famously have | ||
:<math> | :<math> | ||
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In projective space, there is an analogous formula, using the wedge product instead. | In projective space, there is an analogous formula, using the wedge product instead. | ||
Given some real point <math>j \in \mathbb{R^n | Given some real point <math>j \in \mathbb{R}^n</math> with homogeneous coordinates <math>y</math>, and a linear subspace <math>P \in \mathrm{Gr} (k, n)</math> with Plücker coordinates <math>X</math>, we define the projective distance as | ||
:<math> | :<math> | ||