# Orthogonal Vector Space

## Orthogonal Vector Space

A Cartesian plane in which the two axes of the vector space are perpendicular.

### Examples

$$\overrightarrow{v}\perp \overrightarrow{u}$$ and $$m\left ( \overrightarrow{v} \right )\neq m\left ( \overrightarrow{u} \right )$$

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

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