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Is this MathWorld page wrong? (it's about hyperplanes)

  1. Apr 19, 2009 #1
    Here's the page: http://mathworld.wolfram.com/Hyperplane.html

    They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?
     
  2. jcsd
  3. Apr 20, 2009 #2

    CompuChip

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    Let n = 2, a1 = a2 = 1. If I rename x1 = x and x2 = y, then according to you only
    x + y = 0
    defines a line (hyperplane) but
    x + y = 1
    doesn't?

    [edit]I see your point. Probably they should write that it is ... isometric (is that the word here? it's just a line through the origin translated by a constant vector) to a genuine co-dimension one subspace[/edit]
     
    Last edited: Apr 20, 2009
  4. Apr 20, 2009 #3

    matt grime

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    Affine is the word you're looking for: things that look like translations of vector subspaces.
     
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