# What is the sigma representation of adding two or more vectors with an identical number of dimensions into one vector?

What is the sigma representation of adding two or more vectors with an identical number of dimensions into one vector?

For example, something like this: $$[x_1,y_1,z_1,\dots,n_1]+[x_2,y_2,z_2,\dots,n_2]+[x_3,y_3,z_3,\dots,n_3]+\dots+ [x_m,y_m,z_m...n_m] \\= \begin{bmatrix}\bigg(\displaystyle\sum_{i=1}^{m} x_i \bigg),\bigg( \displaystyle\sum_{i=1}^{m} y_i \bigg),\bigg(\displaystyle\sum_{i=1}^{m} z_i\bigg)..,\bigg(\displaystyle\sum_{i=1}^{m} n_i\bigg)\end{bmatrix}$$

But i am sure there's a shorter formal way of doing it

• You can just type your LaTeX into the question box and it will render with MathJax. No need to paste an image from codecogs. – Matthew Leingang Sep 27 '17 at 23:21
• @MatthewLeingang It doesn't look the same – soundslikefiziks Sep 27 '17 at 23:25
• I've gone ahead and done it. You just need to enclose the displayed math between double-dollar signs. – Matthew Leingang Sep 27 '17 at 23:31
• @MatthewLeingang Awsome, it looks exactly the same with MathJax, Thanks. – soundslikefiziks Sep 27 '17 at 23:35

$$\sum_i^m [x_i , y_i, \ldots , n_i]$$ will do the job, assuming your reader knows how to add vectors.

If you're doing this a lot you might want to name the vectors $v_i$.

• I thought about that, but it seemed unclear to me not to include anything that would indicate an addition of the dimensions $$(x_1 +x_2+x_3...)$$ , is this a formal representation ? – soundslikefiziks Sep 27 '17 at 23:41
• You're not adding dimensions. All the vectors have the same dimension, as you know. You aren't (and can't) name the dimension, because you're using $x, y, \ldots , n$ to name the coordinates, rather than going for double subscripts. (Euler would approve - makes for readability.) If you go for double subscripts then it's clear that you are just adding the rows (or columns) of a matrix. – Ethan Bolker Sep 27 '17 at 23:48
• Yes, i meant the addition of the identical dimensions, so what you are suggesting would look like this ? : $$\sum_{i=1}^{m} [[v_i]_1,[v_i]_2,[v_i]_3..,[v_i]_n]$$ – soundslikefiziks Sep 28 '17 at 0:06
• Yes, probably without the inner brackets. Perhaps $v_{i,j}$. But your $x,y$ etc is OK. – Ethan Bolker Sep 28 '17 at 0:15
• But wouldn't this still force me to elaborate with the addition of : $$=[x_1,y_1,z_1,\dots,n_1]+[x_2,y_2,z_2,\dots,n_2]+[x_3,y_3,z_3,\dots,n_3]+\dots+ [x_m,y_m,z_m...n_m]$$ – soundslikefiziks Sep 28 '17 at 0:36