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I can think of multiple ways of writing the sum of a vector $\mathbf{v}$'s elements, but is there a standard operator for this?
Using "programming" notation it is typically sum($v$), but this seems informal. Perhaps just $\mathbf{1}^T \mathbf{v}$ or $\mathbf{1} \cdot \mathbf{v}$?
$\sum_{i=1}^n v_i$ is the most widely accepted and understood notation.
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Oct 28, 2016 at 6:25
If you use the euclidean 1-norm and you want the sum of the absolute values of the entries of $\vec{v}$ (or $v_i\geq 0$ ) you can take $\| \vec{v}\|_1$. Otherwise you can use $sum\{\vec{v} \}$ or $trace( diag\{ \vec{v}\})$. But I guess $sum\{\vec{v}\}$ would be the more "standard" notation.
For the Euclidean space $R^n$, where the inner product is given by the dot product: $$\langle(x_1, x_2, ..., x_n), (y_1, y_2, ..., y_n)\rangle = x_1 y_1 + x_2 y_2 + ... + x_n y_n$$ See Inner Product - Wolfram MathWorld, http://mathworld.wolfram.com/InnerProduct.html
So we can use $\vec{1}$ to form a inner product with vector $\vec{v}$: $$\langle\vec{1}, \vec{v}\rangle = v_1 + v_2 + ... + v_n$$ or $$\langle\vec{v}, \vec{1}\rangle = v_1 + v_2 + ... + v_n$$
Pay attention to the dimension of $\vec{1}$, which be the same as that of $\vec{v}$.
Although the summation is also widely accepted, the notation $\mathbf{1}^\top \mathbf{v}$ is well established (and much more elegant since it avoid the clumsy summation symbol).
