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I have a vector of numbers that looks like this:

[1, 2, 3, 4, 5]

For every number the vector, I would like to multiply each number by every other number and find the sum:

1*1 + 1*2 + 1*3 + 1*4 + 1*5 + 2*1 + 2*2 + 2*3 + 2*4 + 2*5 + ... + 5*5

How can I write this in math notation?

user1728853
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    $$(1+2+3+4+5)^2$$ – Karl Hardr Jun 18 '13 at 13:17
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    If you want to keep a vector notation, $$\left(\begin{pmatrix} 1 \ 2 \ 3 \ 4 \ 5\end{pmatrix}^{\mathrm{T}}\begin{pmatrix} 1 \ 1 \ 1 \ 1 \ 1\end{pmatrix}\right)^2$$ or even, for general $x\in\mathbb{R}_+^n$, $\lVert x \rVert_1^2$. – Clement C. Jun 18 '13 at 13:22
  • Thanks. This was a trivialized example, I'm actually looking for a way to denote this with more complex expressions. – user1728853 Jun 18 '13 at 13:23
  • Just out of curiosity, why do you want more complex expressions? Generally in math you want an expression to be as simple as possible. – rurouniwallace Jun 18 '13 at 13:25
  • What I mean is that the actual math I am doing for each pairwise combinations is more complex than simply squaring each number. – user1728853 Jun 18 '13 at 13:27

1 Answers1

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$\sum_{i=1}^5 \sum_{j=1}^5 ij$.

However, you can also give the array $v$ values $v_i$ other than the index $i$. Then you would write:

$\sum_{i=1}^5 \sum_{j=1}^5 v_iv_j$.

Loki Clock
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