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Summation Notation Ambiguity

  1. Mar 13, 2010 #1
    I am working on a problem that uses the notation:

    \sum_{i,j=1}^n A_{i,j}

    Where A is an (n x n) matrix. I am a little unsure of what the summation is over, due to the odd notation "i,j = 1". My first guess is that this is shorthand for

    \sum_{i=1}^n \sum_{j=1}^n A_{i,j}

    But I am wondering if it could also mean the sum over the diagonal elements of the matrix, i.e.:

    \sum_{i=1}^n A_{i,i}

    I am guessing it is the first, but I want to make absolutely sure.
  2. jcsd
  3. Mar 13, 2010 #2


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    Yes, your first guess is the standard interpretation.
  4. Mar 13, 2010 #3
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