Eigenvector Demo

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.]