Dot Products as Matrix Multiplication

Theorem

Form	Dot Product
$\mathbf{u},\mathbf{v}$ col matrix	$\mathbf{u}\cdot \mathbf{v}={\mathbf{u}}^T\mathbf{v}={\mathbf{v}}^T\mathbf{u}$
$\mathbf{u}$ row matrix $\mathbf{v}$ col matrix	$\mathbf{u}\cdot \mathbf{v}=\mathbf{uv}={\mathbf{v}}^T\mathbf{u}$
$\mathbf{u}$ col matrix $\mathbf{v}$ row matrix	$\mathbf{u}\cdot \mathbf{v}=\mathbf{vu}={\mathbf{u}}^T{\mathbf{v}}^T$
$\mathbf{u},\mathbf{v}$ row matrix	$\mathbf{u}\cdot \mathbf{v}=\mathbf{u}{\mathbf{v}}^T=\mathbf{v}{\mathbf{u}}^T$