# Definition:Vector Sum

## Definition

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

Then the (vector) sum of $\mathbf x$ and $\mathbf y$ is given by:

$\mathbf x + \mathbf y := \tuple {x_1 + y_1, x_2 + y_2, \ldots, x_n + y_n}$

Note that the $+$ on the right hand side is conventional addition of numbers, while the $+$ on the left hand side 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 known as

A vector sum is also frequently seen referred to as a resultant.