example of non linear matrix transformation Could you give me an example of non linear transformation matrix? What is the difference between linear and non linear transformation matrix?
 A: Here's an example. Any 3x3 matrix (using homogeneous coordinates) that represents a translation of 2D points will be a non-linear transformation.  So take the point $(x,y)$ and convert to homogeneous coordinates $(x,y,1)$.  Consider the transformation represented by the matrix:
$\left[ \begin{array}{ccc}
1 & 0 &  h\\
0 & 1 & k\\
0 & 0 & 1 &
\end{array} \right]$
This transformation will map $(x,y,1)$ to $(x+h, y+k,1)$, which represents the point $(x+h,y+k)$. 
$(x,y) \rightarrow (x+h,y+k)$ is a transformation that is not linear, and it is represented by the above matrix.
However, the standard way to represent a transformation with a matrix will always yield a linear transformation.
A: Unless you're not studying linear algebra, every transformation given by a matrix is linear. This is easy to see, from the definition of how you view a matrix as a function, namely, for a $n\times m$ matrix $A$ you can have it act on vectors $v$ of length $m$ by multiplication $A(v) = A\cdot v$, but of course it follows from the definition of matrix multiplication that this function is linear.
