A linear Mapping $f$ from $\R^n$ to $\R^m$ can be defined as follows:
<aside> 💡 $f(x_1,x_2,...,x_n)= (\sum_{j=1}^na_{1j}x_j,\sum_{j=1}^na_{2j}x_j,......,\sum_{j=1}^na_{mj}x_j)$
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where the coefficients $a_{ij}s$ are real numbers(scalars).
A linear mapping can be thought of as a collection of Linear Combinations.
It follows that a linear mapping satisfies linearity, i.e. for any $c\in\R$ (scalar):
<aside> 💡 $f(x_1+cy_1,x_2+cy_2,.....,x_n+cy_n)=f(x_1,x_2,....,x_n)+cf(y_1,y_2,....,y_n).$
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