Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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

    [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

    User Avatar
    Science Advisor
    Homework Helper

    Affine is the word you're looking for: things that look like translations of vector subspaces.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook