EigenExplorer is a Java applet designed to explore the the relationships between a matrix A, a vector x, and the matrix-vector product Ax.
The blue line represents the vector x. It will always appear as a line from the center to a point on the unit circle. You can change the vector x by moving the mouse around while holding down the button.
The red line represents the vector Ax, formed by left-multiplying x by A. The length of Ax changes as x changes.
The dark gray circle in the center of the applet represents the unit circle. The light gray ellipse (activated by pressing the Trace Ax Vector checkbox) shows the image of the unit circle under the transformation given by the matrix A.
To change the matrix, change the individual values in the upper left-hand corner of the applet.
This applet is part of a package called LAVA: The Linear Algebra Visualization Assistant.