What Does Linearity Mean?
Linearity describes a special property of a transformation T from Rn to Rm such that any linear combination of inputs yields the respective linear combination of their outputs. A transformation such as this remains closed under the operations of addition and scalar multiplication.
Example of a Linear Transformation (system)
The following linear transformation takes any vector in R2 and maps it to another vector in R2 of same length rotated 45 degrees counter clockwise.
$ \ T(X)= \mathbf{A}X $
where $ \mathbf{A} = \begin{bmatrix}cos(\pi/2) & sin(\pi/2) \end{bmatrix} $
