Definition:Vector Length

Definition
The length of a vector $\mathbf v$ in a normed vector space $\struct {V, \norm {\, \cdot \,} }$ is defined as $\norm {\mathbf v}$, the norm of $\mathbf v$.

Also denoted as
$\size {\mathbf v}$ is often also seen for the length of $\mathbf v$.

Some authorities state that this is not recommended since it can lead to confusion with absolute value.

is less convinced that this is a problem, and both notations can be found here.

It is commonplace to use the non-bold italic form of the symbol for the length, hence using $v$ for the length of $\mathbf v$.

Some sources use $\bmod \mathbf v$ for the length of $\mathbf v$.

Also see

 * Distance Formula