Visual SVD Java Applet - Andrew Trusty (gtg877q)
 
Source
The JAR archive of the source and class files are available here VisualSVD.jar, it includes the JAMA Package and my modified version of the Java 2D Graph Package classes.

The source of the applet alone is available here, VisualSVD.java, it requires the JAMA Package and my modified version of the Java 2D Graph Package classes to compile.
Usage
Enter the values you wish to use for the matrix A in the available textfields and click Calculate SVD & Graph to see the results. The singular value decomposition of A will appear in the textfields to the left of A in the form VD(U^transposed) and the Linear Transformation by A on the unit circle will be displayed on the right graph. Some working values are used by default.

The blue lines appearing on the Unit Circle are the unit vectors u1 and u2, those on the Linear Transformation are the vectors v1 and v2 representing the major and minor axes and the points at which the maximum and minimums are obtained.

By dragging your mouse cursor anywhere on the Unit Circle graph the corresponding vector to the one that appears following your mouse will be drawn on the Linear Transformation graph to the right, allowing you to visualize the maximization/minimization procedure.