Matrix multiplication

Recall matrix multiplication. The value at row $i$ column $j$ of $\M{M}$ equals the dot product of row $i$ of $\M{A}$ with column $j$ of $\M{B}$.

\[\M{M} = \M{A}\cdot \M{B}\] \[\begin{squeezematrix} m_{ 0} & m_{ 4} & m_{ 8} &m_{12} \\ m_{ 1} & m_{ 5} & m_{ 9} &m_{13} \\ m_{ 2} & m_{ 6} & m_{10} &m_{14} \\ m_{ 3} & m_{ 7} & m_{11} &m_{15} \\ \end{squeezematrix}= \begin{squeezematrix} a_{ 0} & a_{ 4} & a_{ 8} &a_{12} \\ a_{ 1} & a_{ 5} & a_{ 9} &a_{13} \\ a_{ 2} & a_{ 6} & a_{10} &a_{14} \\ a_{ 3} & a_{ 7} & a_{11} &a_{15} \\ \end{squeezematrix}\cdot \begin{squeezematrix} b_{ 0} & b_{ 4} & b_{ 8} &b_{12} \\ b_{ 1} & b_{ 5} & b_{ 9} &b_{13} \\ b_{ 2} & b_{ 6} & b_{10} &b_{14} \\ b_{ 3} & b_{ 7} & b_{11} &b_{15} \\ \end{squeezematrix}\] \[\begin{array}{ccccccccc} m_{0} &=& a_{0}\cdot b_{0} &+& a_{4}\cdot b_{1} &+& a_{8}\cdot b_{2} &+& a_{12}\cdot b_{3} \\ m_{1} &=& a_{1}\cdot b_{0} &+& a_{5}\cdot b_{1} &+& a_{9}\cdot b_{2} &+& a_{13}\cdot b_{3} \\ m_{2} &=& \mathit{etc\ldots} \\ \end{array}\]