Full Diagonalization

Full diagonalization of matrices is a powerful numerical method for understanding small quantum systems, especially when the excited states of a quantum system is required. The last step of the Lanczos algorithm also requires a full diagonalization of a small matrix formed at the end of the iterative process.

We will focus on the dicussion of two numerical methods Jacobi rotation and QR factorization. However, actual calculations in ALPS are carried out with the LAPACK software package, which is specialized for linear algebra.