Rabbits Three

$(av) \otimes w = v \otimes (aw) = a(v \otimes w) \: \: a \in \mathbb{C}$

$(v_1 + v_2) \otimes w = v_1 \otimes w + v_2 \otimes w$

$v \otimes (w_1 + w_2) = v \otimes w_1 + v \otimes w_2$

i .. i .. i

$v = \displaystyle \sum_i v_i e_i$

$w = \displaystyle \sum_j w_j f_j$

$\displaystyle v \otimes w = (\sum_i v_i e_i) \otimes (\sum_j w_j f_j) = \sum_i \sum_j v_i w_j e_i \otimes f_j$