TeX source:

\left\langle \sum_ia_i|v\rangle_i\otimes|w\rangle_i \Bigg| \sum_jb_j|v'\rangle_j\otimes|w'\rangle_j \right\rangle \equiv \sum_{i,j}a_i^\ast b_j\langle v_i|v'_j \rangle\langle w_i|w'_j \rangle.