This worksheet illustrates the effect of a linear transformation in [math]R^2[/math] on the unit circle/unit disk.
Students can drag a point on the unit circle and its image under the transformation will automatically update. Students can geometrically identify the eigenvectors by observing when the vector and its image are parallel, and the eigenvalues by their relative lengths.
The effect of the transformation as a geometrical transformation can be illustrated by clicking 'Show clockface'. This will animate the effect of the transformation on the unit disk (shown as a clockface). Eigenvectors can be identified geometrically as the axes of dilation or reflection.
Note: Eigenvectors and eigenvalues are not calculated & displayed correctly in some cases. This is a bug.