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Affine plane

  1. Mar 14, 2010 #1
    In an affine plane of order n, prove that each line contain exactly n points
  2. jcsd
  3. Mar 14, 2010 #2
    Hi, I will try to help you out :)

    Lets consider an n-dimensional Euclidean space [tex]E_{n}[/tex] and by means of abstraction we develop the algebra of general affine tensors.

    An orthonormal system [tex] e_{j} [/tex] in [tex] E_{n}[/tex] consists of n mutually orthogonal unit vectors. Any orthonormal system [tex] {\bar{e}_{j}} [/tex] may be obtained from the first by means of the linear transformation

    [tex] \bar{e}_{j} = \sum^{n}_{h= 1} a_{ j, h} e_{h} (j = 1, ....., n) [/tex]

    provided that the coefficients [tex] a_{jh}[/tex] satisfy the orthogonality condition

    [tex]\delta _{j,k} = \sum^{n}_{h=1} a_{j,h} a_{k, h} (j, k = 1, ...,n), [/tex]

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