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.