Please enter the four matrix entries in the boxes above. Be sure to press enter after each entry. Now press the mouse anywhere on the applet in order to draw a vector and that vector times the matrix. Experiment until this vector lines up with the other one, if possible. Now you have found an eigenvector of that matrix.
An eigenvector v of a matrix A satisfies the following equation: Av=cv where c is a scalar, actually c is the eigenvalue of the matrix A. If a matrix has an eigenvector, then it has an infinite number of them. To see this, simply take your original vector v and multiply it by any scalar you want (rather lengthen or shorten your vector v on the screen), this is another eigenvector. This demo gives you a graphical idea of what an eigenvector is, rather than reading tedious material from a linear algebra book!
[Note added later: The matrix transformation in this demo is apparently v -> vA rather than v -> Av as stated; equivalently, A should be transposed.]
JAVA SOURCE CODE