This applet shows the behaviour of a linear mapping in two dimensions. The image vector is shown in red, and the black vector can be displaced by click and drag.
The transformation matrix is editable.
1. Construct the image of the vector (0,0). What happens?
2. Construct the image of the vector (1,1), and afther that, the image of the vector (2,2). What happens? Why?
3. Can you estimate, just playing with the vector, some eigenvector? Remember that not all linear mappings have real eigenvectors.
Eigenvalues and eigenvectors.