this is for holding javascript data
Benedict Irwin edited Project.tex
over 9 years ago
Commit id: a0c68ed212c2c22d2d352e82e1cbc7a9e983ff8b
deletions | additions
diff --git a/Project.tex b/Project.tex
index 1626b0e..ef7b2b5 100644
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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}