1. Apr 19, 2009 #1

   samh

   

   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?

    

   samh, Apr 19, 2009
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3. Apr 20, 2009 #2

   CompuChip

   

   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
   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

   CompuChip, Apr 20, 2009
4. Apr 20, 2009 #3

   matt grime

   

   Science Advisor

   Homework Helper

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

    

   matt grime, Apr 20, 2009

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