Matrices can be useful to describe transformations.[br][br]Drag points A1 and A2 to define the transformation matrix A.[br][br]Then click "Show Vectors" to see where a vector [b]x[/b] will end up after it has been transformed by A.[br][br]Move the vector [b]x[/b] around to see where the transformed vector A[b]x[/b] will end up.[br][br]Certain vectors will put the transformed vector A[b]x[/b], the original vector [b]x[/b] and the origin O in perfect alignment (i.e. they are [i]collinear[/i]). We call these vectors[b] eigenvectors[/b].[br][br]When this happens, this must mean that the transformed vector A[b]x[/b] is just some scalar multiple of the original vector i.e. [math]\lambda[/math][b]x[/b]. We call this scalar [math]\lambda[/math] an [b]eigenvalue[/b].