https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab | BV1ys411472E

Linear? → 1. lines remain lines 2. origin remains fixed

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⏱️timestamp ← You only need to record where the two basis vectors (i-hat and j-hat) each land, and everything else will follow from that. (this is great. It helps me understand how to describe transformation numerically.)

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Every time you see a matrix, you can interpret it as a certain transformation of space.

将矩阵看作空间的变换

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The determinant of a transformation (理解它的意义，比计算本身重要得多)

矩形面积的变化 / 立方体体积的变化 / …

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Duality

Dotting two vectors together is a way to translate one of them into the world of transformations. 两个向量点乘，就是将其中一个向量转化为线性变换。

$$ \begin{bmatrix}a & b \end{bmatrix} \longleftrightarrow \begin{bmatrix}a \\ b \end{bmatrix} $$

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