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Extremelly basic doubt

  1. Mar 29, 2012 #1
    Hi. What does that mean when we see:

    $$\mathbb{K}$$ what set is that? definately not the reals, integers, etc.
    and
    $$\mathbb{R}^n$$ Is that the reals or what?

    Thanks!
     
  2. jcsd
  3. Mar 29, 2012 #2
    the blackboard K is often used to refer to an arbitrary field. If you encounter it somewhere it should be stated what is meant by it.

    The blackboard R^n just means n-dimensional real space. So basically (up to linear isomorphism) the unique n-dimensional vector space over the real numbers.
     
  4. Mar 29, 2012 #3
    Thank you!!
     
  5. Mar 29, 2012 #4

    HallsofIvy

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    A tiny disagreement. R^n is the set of order n-tuples of real numbers. It becomes a vector space only with the convention that "sum" and "scalar multiplication" are "coordinate wise". Yes, that is the "natural" convention but it separate from just "R^n".
     
  6. Mar 29, 2012 #5
    You are right of course. Naturally my response was in terms of the vector space since this is the first definition I saw. You could also assume this and express that you are only talking strictly as the n-tuples of real numbers by mentioning you use the bare set underlying the vector space. I think in most literature the vector space (indeed also the natural topological, norm, inner product, Lie group and manifold (symplectic, smooth, Riemannian)) structure are assumed when used. A thing that might be stated explicitely is any algebra structure.

    So immediately when I see that symbol these things I also assume, but it might pay to be a bit more reserved about this.
     
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