# Normed Vector Space

## Normed Vector Space

Vector space in which the vectors of the basis have the same length.

### Example

In this case, the vector space may also be orthogonal; if so, it is said to be orthonormal, as in the following example:

$$\overrightarrow{j} \perp \overrightarrow{i}$$ and $$m\left ( \overrightarrow{j} \right )=m\left ( \overrightarrow{i} \right )$$