Q: Unit Square and Matrices, how is it plotted? I have a question on how unit square is mapped on a graph. I have a matrix transformation of M. Take an example from: http://www.ams.org/samplings/feature-column/fcarc-svd
\begin{equation*}
 M=\begin{bmatrix}
    3&0\\
    0&1
  \end{bmatrix}
\end{equation*}
It said that taking a point (x,y), and transformating it into another point. With the unique square looks like:
\begin{equation*}
 (x,y)=\begin{bmatrix}
    X\\
    Y
  \end{bmatrix}=\begin{bmatrix}
    1\\
    1
  \end{bmatrix}
\end{equation*}
However, this looks like a vector, and and it points to (1,1) starting from (0,0). How does this get mapped into a square?


A: You need to take every point inside of the square and map it using the given transformation matrix. Obviously, you have an infinite number of points to do so. The trick is, for certain transformations, like yours, you can take only vertices and map them and then claim that all points inside of the square will be inside of the shape that you get if connect those 4 mapped points. 
