# Linear Transformation (선형변환)

Definition of Linear Transformation (Linear Map)
Let $V$ and $W$ be vector spaces over the same field $K$. A function $T : V → W$ is said to be a linear transformation (or a linear map) if for any two vectors $\textbf{x}$ and $\textbf{y}$ in $V$ and any scalar $\alpha$ in $K$, the following two conditions are satisfied:

$T(\textbf{x} + \textbf{y})=T(\textbf{x})+f(\textbf{y})$     : additivity
$T(\alpha \textbf{x}) = \alpha T (\textbf{x})$     : homogeneity of degree 1.