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fix katex complaining

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Rachel Lambda Samuelsson 2024-07-17 22:30:25 +02:00
parent 7faa512335
commit e2cf382fbd
1 changed files with 9 additions and 3 deletions
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src/posts/a-favourite-proof-of-mine.md
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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
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? 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?
$$ $$
S \left(\begin{bmatrix} a & b \end{bmatrix}\right) \\ S \left(\begin{bmatrix} a & b \end{bmatrix}\right)
+ S\left(\begin{bmatrix} c & d \end{bmatrix}\right) \\ $$
= \begin{bmatrix} b a + b \end{bmatrix} \\ $$
+ S\left(\begin{bmatrix} c & d \end{bmatrix}\right)
$$
$$
= \begin{bmatrix} b a + b \end{bmatrix}
$$
$$
+ \begin{bmatrix} d c + d \end{bmatrix} + \begin{bmatrix} d c + d \end{bmatrix}
$$ $$