Department of Computer Science

Laboratory exercise seven involves studying the eigenvalues and eigenvectors of a real n by n matrix. We will perform the following tasks:

1. Write a program which will implement the power method for the largest (magnitude) eigenvalue of the matrix. Display the eigenvalue and a corresponding eigenvector.
2. Use your matrix inverse program to find the inverse of the matrix.
3. Use the power method on the inverse to find the largest eigenvalue of the inverse. Verify that the reciprocal of this eigenvalue is an eigenvalue of the original matrix.

Make sure you display sufficient information so issues of convergence can be studied.