The dot product of two vectors is defined as following: $$ \langle \vec v, \vec u \rangle = \left< \begin{pmatrix} v_1 \\ v_2 \\ \dots \\ v_n \end{pmatrix}, \begin{pmatrix} u_1 \\ u_2 \\ \dots \\ u_n \end{pmatrix} \right> = v_1 \cdot u_1 + v_2 \cdot u_2 + \dots + v_n \cdot u_n $$
Still the multiplication of transposition of $\vec v$ and u gives: $$ \vec v^T \cdot \vec u = (v_1, v_2, \dots, v_n) \cdot \begin{pmatrix} u_1 \\ u_2 \\ \dots \\ u_n \end{pmatrix} = v_1 \cdot u_1 + v_2 \cdot u_2 + \dots + v_n \cdot u_n $$
so the result is the same!
It may be just a silly observation but I'm just surprised because I have never seen using it.
Are these two notations the same thing or is there something important in their definitions that don't allow interchanging them?