This applet is a fancier version of the linear transformations applet. There are three new features. Firstly, the eigenvalues of the matrix are computed near the bottom of the applet. (Note how the sum of the two eigenvalues is the trace of the matrix, and the product of the two eigenvalues is the determinant of the matrix). Secondly, if the eigenvalues are real, the eigenvectors are drawn in purple. In most cases the eigenspaces are just lines, though if the matrix is a multiple of the identity matrix then every vector is an eigenvector. Note that if v is a vector in an eigenspace, then Tv is just the same as v but dilated by an eigenvalue lambda. Thirdly, one can drag the blue and green dots on the right-hand grid to alter the linear transformation. This applet was written by Kim Chi Tran.