Purpose: To see what an eigenvector is in two dimensions.
The vector u is being multiplied by the matrix shown, and the resulting vector is shown in red. Change the vector u by dragging the tip to a different location.
See that multiplying by the matrix will change the direction and length of a vector.

1. Find two different u vectors whose directions are unaffected by multiplication by the matrix. These vectors are called eigenvectors for the matrix.
2. Compare the lengths of the eigenvectors before and after multiplication by the matrix. If the eigenvector grew by a certain factor, that factor is called the eigenvalue for the eigenvector.