Scaling Means To Multiply A Vector

To “Scale” a vector means to multiply it by a variable. Effectively, what you are doing when scaling a vector is to stretch it out over a graph by the variable.

The variables in linear algebra that you are multiplying by are called “Scalars”.

Some Examples:

$\left[\begin{array}{c}1\\ 2\end{array}\right]\times 2=\left[\begin{array}{c}2\\ 4\end{array}\right]$

$\left[\begin{array}{c}1\\ 2\end{array}\right]\times 1/3=\left[\begin{array}{c}0.33\\ 1.33\end{array}\right]$

$\left[\begin{array}{c}1\\ 2\end{array}\right]\times -1=\left[\begin{array}{c}-1\\ -2\end{array}\right]$

Notice in the last example that the negative is applied to both coordinates in the vector. That is because scaling by a negative effectively reverses the course of the directions.

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Connections

Vectors Can Be Summed Because They Are Movement

Link Explanation: As directional movement, vectors can also be multiplied, which creates a “stretching” effect on the distance that the vectors represent.

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Reference

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