Examples

[latex]\overrightarrow{v}\perp \overrightarrow{u}[/latex] and [latex]m\left ( \overrightarrow{v} \right )\neq m\left ( \overrightarrow{u} \right )[/latex] In this case, the vector space can also be normed; if so, it is said to be orthonormal, as in the following example: [latex]\overrightarrow{j} \perp \overrightarrow{i}[/latex] and m([latex]\overrightarrow{j}[/latex]) = m([latex]\overrightarrow{i}[/latex])