Definition:Vector Subtraction

Definition
Let $\struct {F, +_F, \times_F}$ be a field.

Let $\struct {G, +_G}$ be an abelian group.

Let $V := \struct {G, +_G, \circ}_R$ be the corresponding vector space over $F$.

Let $\mathbf x$ and $\mathbf y$ be vectors of $V$.

Then the operation of (vector) subtraction on $\mathbf x$ and $\mathbf y$ is defined as:
 * $\mathbf x - \mathbf y := \mathbf x + \paren {-\mathbf y}$

where $-\mathbf y$ is the negative of $\mathbf y$.

The $+$ on the is vector addition.