Eigenvectors and Eigenvalues

Matrices can be useful to describe transformations. Drag points A1 and A2 to define the transformation matrix A. Then click "Show Vectors" to see where a vector x will end up after it has been transformed by A. Move the vector x around to see where the transformed vector Ax will end up. Certain vectors will put the transformed vector Ax, the original vector x and the origin O in perfect alignment (i.e. they are collinear). We call these vectors eigenvectors. When this happens, this must mean that the transformed vector Ax is just some scalar multiple of the original vector i.e. x. We call this scalar an eigenvalue.