Mathematical Methods of Physics: For Undergraduate

If \(\vec{u},\vec{v} \in \vec{V_{n}}\) then there exists vectors \(\alpha (\vec{u}+\vec{v}){,} (\alpha+\beta)\vec{u}\text{,}\) and \(\alpha(\beta\vec{u})\) in \(V_{n}\) such that \(\alpha (\vec{u}+\vec{v}) = \alpha \vec{u}+\alpha \vec{v})\text{;}\) \((\alpha+\beta)\vec{u} = \alpha\vec{u}+\beta\vec{u}\text{,}\) and \(\alpha(\beta\vec{u}) = (\alpha\beta)\vec{u}\) where \(\alpha\) and \(\beta\) are two scalars ( real or complex numbers).

For the zero and unit vectors in \(V_{n}\) there exists the following products \(0.u=0\) and \(1.u=u\text{.}\)