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Summation notation problem

  1. Jan 9, 2014 #1
    Hi

    I have a text book which uses the notation:

    [itex]\sum\limits_{i\neq j}^N a_i a_j[/itex]

    I can't find anywhere what this actually means. Is it equivalent to:

    [itex]\sum\limits_{i}^N \sum\limits_{j}^N a_i a_j[/itex]

    where j can't equal i?

    Thanks.
     
  2. jcsd
  3. Jan 9, 2014 #2
    It's just the sum of all ##a_{i}a_{j}## when i does not equal j.

    You can put pretty much any condition you want in that space, though I see it abused more often for unions and intersections of sets.
     
  4. Jan 9, 2014 #3

    Mark44

    Staff: Mentor

    Yes, pretty much. For example, if N = 3, and both indexes start at 1, then the summation expands to a1a2 + a1a3 + a2a1 + a1a3 + a2a3 + a3a2. The terms that are omitted are a12, a22, and a32.
     
  5. Jan 10, 2014 #4
    Okay, thanks.
     
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