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.