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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?

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    $\begingroup$ $$(1+2+3+4+5)^2$$ $\endgroup$
    – Karl Hardr
    Commented Jun 18, 2013 at 13:17
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    $\begingroup$ 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 $x\in\mathbb{R}_+^n$, $\lVert x \rVert_1^2$. $\endgroup$
    – Clement C.
    Commented Jun 18, 2013 at 13:22
  • $\begingroup$ Thanks. This was a trivialized example, I'm actually looking for a way to denote this with more complex expressions. $\endgroup$ Commented Jun 18, 2013 at 13:23
  • $\begingroup$ Just out of curiosity, why do you want more complex expressions? Generally in math you want an expression to be as simple as possible. $\endgroup$ Commented Jun 18, 2013 at 13:25
  • $\begingroup$ What I mean is that the actual math I am doing for each pairwise combinations is more complex than simply squaring each number. $\endgroup$ Commented Jun 18, 2013 at 13:27

1 Answer 1

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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:

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

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