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B What does this set notation mean?

  1. Mar 12, 2016 #1
    $$
    A \oplus B
    $$

    where A and B are sets
     
  2. jcsd
  3. Mar 12, 2016 #2

    HallsofIvy

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    That is not a standard notation for sets. It can mean a direct sum for sets with sum kind of "sum" defined, such as vector spaces. Is that what you mean?
     
  4. Mar 12, 2016 #3
    Actually, yes, in the context it was used the sets in question are subspaces of a vector space.

    The context is page 137 here http://perso.crans.org/lecomtev/articles/Brian_Hall_Quantum_Theory_for_Mathematicians_2013.pdf [Broken]
     
    Last edited by a moderator: May 7, 2017
  5. Mar 12, 2016 #4

    PeroK

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    https://en.wikipedia.org/wiki/Hilbert_space#Direct_sums
     
    Last edited by a moderator: May 7, 2017
  6. Mar 12, 2016 #5
  7. Mar 12, 2016 #6

    HallsofIvy

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    The "direct sum" of two vector spaces, A and B, (both subspaces of some vector space, V) is the smallest subspace that contains all the vectors in both A and B. Another way of doing that is to construct bases for both A and B, combining them and then reducing to a set of independent vectors to get a basis for [itex]A\oplus B[/itex].
     
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