Multidimension Linear Transformation

Linear Maps can have multidimensional inputs and output vectors, so long as they satisfy:

• Additivity
• Homogeneity In their respective dimension

2D Linear Transformation

Where $T(x,y):V^2\to V^2$

Proving 2D Linear Transformation

1. Show Additivity ($\forall c\in \mathbb{F},cT(x,y)=T(cx,cy)$)
2. Show Homogeneity ($\forall x_1,y_1,x_2,y_2\in V,T(x_1+x_2,y_1+y_2)=T(x_1,y_1)+T(x_2,y_2)$)