Eigenvalues are important in many branches of the physical sciences; they make it possible to find coordinate systems in which the transformation in question takes on a more simple form. A number LAMBDA is called an eigenvalue of a linear transformation of A if there exists a vector x not equal to 0 such that A(x)= (LAMBDA)x. The vector x is then called an eigenvector of the transformation A belonging to LAMBDA.

The following instructions will verify an eigenvalue LAMBDA and a corresponding eigenvector x if Ax - (LAMBDA)x = 0.