Definition:Vector Length/Real Vector Space

Example of Vector Length

Let $\mathbf v$ be a vector represented in the real $n$-space $\R^n$ by an ordered $n$-tuple of components $\tuple {v_1, v_2, \ldots, v_n}$.

The length of $\mathbf v$ is defined as:

$\norm {\mathbf v} = \ds \sqrt {\sum_{i \mathop = 1}^n v_i^2}$

Also see

• Distance Formula