Benedict Irwin edited Project.tex  over 9 years ago

Commit id: a0c68ed212c2c22d2d352e82e1cbc7a9e983ff8b

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We have vector dot product \begin{equation}  \begin{bmatrix}  a & b  \end{bmatrix}  \cdot  \begin{bmatrix}  c \\ d  \end{bmatrix} \begin{bmatrix}a&b\end{bmatrix}\cdot\begin{bmatrix}c\\d\end{bmatrix}  =ac+bd  \end{equation} 

M=(v\cdot u)\otimes(v^T\cdot u^T)  \end{equation}  With this concept in mind let us examine the matrix muliplication operation \begin{equation}  \begin{bmatrix}  a & b \\ c & d  \end{bmatrix}  \begin{bmatrix}  e & f \\ g & h  \end{bmatrix}  =  \begin{bmatrix}  ae+bg & af+bh \\ ce+dg & cf+dh  \end{bmatrix}  =  \begin{bmatrix}  \begin{bmatrix}a&b\end{bmatrix}\cdot\begin{bmatrix}e\\g\end{bmatrix}  &  \begin{bmatrix}a&b\end{bmatrix}\cdot\begin{bmatrix}f\\h\end{bmatrix}  \\  \begin{bmatrix}c&d\end{bmatrix}\cdot\begin{bmatrix}e\\g\end{bmatrix}  &  \begin{bmatrix}c&d\end{bmatrix}\cdot\begin{bmatrix}f\\h\end{bmatrix}  \end{bmatrix}  \end{equation}