- #1
Buffu
- 849
- 146
##\begin{align}[A(BC)]_{ij} &= \sum_r A_{ir}(BC)_{rj} \\ &= \sum_r A_{ir} \sum_s B_{rs}C_{sj}\\ &= \sum_r\sum_s A_{ir}B_{rs}C_{sj}\\ &= \sum_{s} (\sum_{r} A_{ir} B_{rs}) C_{sj} \\ &= [(AB) C]_{ij}\end{align}##
How did it went from ##2## to ##3##. In general is there a proof that sums can be switched like this ?
How did it went from ##2## to ##3##. In general is there a proof that sums can be switched like this ?