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projective line
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(Definition)
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A projective line is a subspace of dimension 2 in a vector space. Although the usual notion of lines are 1 dimensional, in projective geometry 1 dimensional subspaces are the correct notion of points, sometimes called projective points. In keeping with expectation, two (projective) points determine a single(projective)
line; that is, two 1-dimensional subspaces span a single 2-dimensional subspace.
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![$ \ell=\{[X,Y,Z,W]\in \mathbf{RP}^3 \pipe Z=W=0\}$](http://images.planetmath.org:8080/cache/objects/5005/l2h/img1.png "$ \ell=\{[X,Y,Z,W]\in \mathbf{RP}^3 \pipe Z=W=0\}$")
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"projective line" is owned by bwebste. [ full author list (3) | owner history (1) ]
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(view preamble)
Cross-references: MA, span, expectation, points, projective geometry, lines, vector space, dimension, subspace
There are 7 references to this entry.
This is version 3 of projective line, born on 2003-10-15, modified 2006-04-17.
Object id is 5005, canonical name is ProjectiveLine.
Accessed 2577 times total.
Classification:
| AMS MSC: | 51E15 (Geometry :: Finite geometry and special incidence structures :: Affine and projective planes) |
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Pending Errata and Addenda
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