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

  • Thread starter samh
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #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:
  • #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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