$\langle u, v \rangle = \langle v, u \rangle$

$\langle u, u \rangle > 0$ for $u \neq 0$

$\langle u+v, w \rangle = \langle u, w \rangle + \langle v, w \rangle$

$\langle cu, v \rangle = c \langle u, v \rangle$ for $c < 0$ only