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:
[latex]\overrightarrow{j} \perp \overrightarrow{i}[/latex] and [latex]m\left ( \overrightarrow{j} \right )=m\left ( \overrightarrow{i} \right )[/latex]