#cheatsheet #mathematic #linear-algebra # [[Epistemic status]] #shower-thought #to-digest # Related - [[en.wikipedia.org - Linear Span - Wikipedia|Linear Span - Wikipedia]] - [[en.wikipedia.org - Linear Subspace - Wikipedia|Linear Subspace - Wikipedia]] # TODO > [!TODO] TODO > generate the cheatsheet with [[GPT3]] # Linear algebra cheatsheet | human | machine | human++ | | --------------- | ----------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | vector | $ \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix} $ | A vector is an ordered list of numbers. In the above example, $\mathbf{x}$ is a vector with $n$ components, $x_1, x_2, \ldots, x_n$. | | scalar addition | $ \mathbf{x} + \mathbf{y} = \begin{bmatrix} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{bmatrix} $ | If $\mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix}$ and $\mathbf{y} = \begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_n \end{bmatrix}$ are two vectors, then their sum is given by $\mathbf{x} + \mathbf{y} = \begin{bmatrix} x_1 + y_1 \\ x_2 + y_2 \\ \vdots \\ x_n + y_n \end{bmatrix}$ | | scalar | | | ![[ln_cheat_sheet.pdf]] https://laurentlessard.com/teaching/ece532/cheat_sheet.pdf ## Random >Modern linear algebra is computational, whereas traditional linear algebra is abstract. >~ [[Cohen M. - Practical Linear Algebra for Data Science]] ## Wonder A tensor in the sky by Escher ![[ddccdc6a-eafd-4e1a-a3b2-ec1584d3d05c-0-1997984393.png]] # External links