Definition:Vector Sum

Definition
Let $\mathbf x = \left({x_1, x_2, \ldots, x_n}\right)$ and $\mathbf y = \left({y_1, y_2, \ldots, y_n}\right)$ be vectors of an $n$-dimensional vector space.

Then the (vector) sum of $\mathbf x$ and $\mathbf y$ is given by:
 * $\mathbf x + \mathbf y := \left({x_1 + y_1, x_2 + y_2, \ldots, x_n + y_n}\right)$

Note that the $+$ on the RHS is conventional addition of numbers, while the $+$ on the LHS takes on a different meaning. The distinction is implied by which operands are involved.

If necessary to distinguish the vector sum operation with other forms of addition, $+$ can be called vector addition.

Also see

 * If the vectors involved are written as column matrices, then vector addition can be understood as Matrix Addition.