How to correctly represent a nested sum

Question

Suppose I have a matrix:

$$ A = \begin{pmatrix} 1 & 4 & 7 \\ 2 & 5 & 8 \\ 3 & 6 & 9 \\ \end{pmatrix} $$ For which i want to sum the elements.

My first inclination is to write:

$$ \sum_j \sum_i A_{i,j} $$

But I am unsure whether this is normally read:

$$ \sum_j \left( \sum_i A_{i,j} \right) $$

Or:

$$ \left(\sum_j \sum_i \right) A_{i,j} $$

Where i intend the latter.

The latter notation means nothing. The former is what you want. First you sum the rows. Then you sum the row sums. This works by associativity of addition. — Emily, Nov 27 '13 at 23:56
OK, you beat me by 1 minute but I posted it as an answer. Sorry! :( — Ahaan S. Rungta, Nov 27 '13 at 23:59

Ahaan S. Rungta · Accepted Answer · 2013-11-30T14:39:12.133

2

The latter notation is meaningless. The first one is correct. However, without the parentheses, it means the same thing. The last one is the big no-no. In other words: $$ \sum_j \sum_i A_{i,j} \equiv \sum_j \left( \sum_i A_{i,j} \right), $$ but you should not write $$ \left( \sum_j \sum_i \right) A_{i,j}. $$

edited Nov 30 '13 at 14:39

answered Nov 27 '13 at 23:58

Ahaan S. Rungta

7,706

How to correctly represent a nested sum

1 Answers1