When performing the eigenvalue decomposition for a small matrix of 2-by-2 or 3-by-3, there is a simple set of steps that we can take to produce our eigenvalues and eigenvectors. When working with larger matrices, this problem is rather tedious and it's best left to a computer to discover the eigenvalues. A study of the algorithms used to discover eigenvalues goes well beyond the scope of this book. We will use the hmatrix library and LAPACK to compute the eigenvalues and eigenvectors of our covariance matrices.