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Quantum states and complex numbers - newbie question

  1. Sep 2, 2011 #1
    this wikipedia article http://en.wikipedia.org/wiki/Qubit says
    i am kind of comfortable with the physics of it, but i am totally lost on the thing about vector space over the complex numbers

    can someone please lend me a hand? it seems that the more i try to read about it, the less i know
  2. jcsd
  3. Sep 2, 2011 #2


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    In general a vector space consists of vectors with scalar multipliers. In two dimensions vectors are of the form (x,y) where x and y are numbers (scalars). For a real vector space x and y will be real numbers and the scalars are real numbers, while for a complex vector space x and y will be complex numbers and the scalars may be complex.. Vectors can be added or subtracted and multiplied by scalars.

    For example Let (x,y) and (u,v) be vectors and a and b scalars, then
    a(x,y) + b(u,v) = (ax+bu,ay+bv).
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