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Linear vs affine

  1. Dec 6, 2011 #1
    The context is polytopes...reading some introductory material.

    It talks about two points in R3, namely p=(1,0,0) and q=(0,1,0)
    and tells me to notice that the linear span of of p and q and the affine span of p and q are not the same.

    Could somebody tell me the difference? Thanks
     
  2. jcsd
  3. Dec 7, 2011 #2

    Stephen Tashi

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    My guess is that the linear span is the set of all linear combinations of p and q and the affine span is the set of all affine linear combinations of p and q. (An affine linear combination requires that the sum of coefficients in the linear combination is 1 )
     
  4. Dec 7, 2011 #3

    micromass

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    The linear span will be the plane <(0,0,0),(1,0,0),(0,1,0)>.
    The affine span will be the line <(1,0,0),(0,1,0)>.

    Do you see why??
     
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