Linear Transformation

• Linear Transformation

 

A mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.

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• Matrix multiplication(The dot product of a vector)

 

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Calculate how similar between X1 & X1, X2 & X1∙∙∙look.

 

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• Linear combination of column vectors

 

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• vector symbol

 

$\stackrel{\to <!--\; \to \; -->}{x}$

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• Linear Transformation

 

 

 

$$\begin{array}{}& A\stackrel{\to <!--\; \to \; -->}{x}=\left[\begin{array}{cc}2& -<!--\; -\; -->3\\ 1& 1\end{array}\right]\left[\begin{array}{c}1\\ 1\end{array}\right]=\left[\begin{array}{c}-<!--\; -\; -->1\\ 2\end{array}\right]\end{array}$$

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Before transform

x : [1, 0]

y : [0, 1]

$\stackrel{\to <!--\; \to \; -->}{x}$ : [1,1]

 

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After transform

x : [2,1]

y : [-3, 1]

$\begin{array}{}A\stackrel{\to <!--\; \to \; -->}{x}\end{array}$ : [-1,2]

 

 

https://angeloyeo.github.io/2019/07/15/Matrix_as_Linear_Transformation.html