fix katex complaining
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@ -61,9 +61,15 @@ In each step we move the window by replacing the first slot in the window by wha
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What does this have to do with mathematics, and this beautiful proof that I have promised? We shall begin to translate this moving window into the language of mathematics, our window is a pair of numbers, so why not represent it as a vector. Furthermore, we may view sliding our window one step as a function $S$ from vectors to vectors. This poses an interesting question: is this function a linear transformation?
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$$
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S \left(\begin{bmatrix} a & b \end{bmatrix}\right) \\
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+ S\left(\begin{bmatrix} c & d \end{bmatrix}\right) \\
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= \begin{bmatrix} b a + b \end{bmatrix} \\
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S \left(\begin{bmatrix} a & b \end{bmatrix}\right)
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$$
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$$
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+ S\left(\begin{bmatrix} c & d \end{bmatrix}\right)
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$$
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$$
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= \begin{bmatrix} b a + b \end{bmatrix}
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$$
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$$
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+ \begin{bmatrix} d c + d \end{bmatrix}
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$$
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