Many generalizations have been made for Fibonacci and Lucas number sequences and many properties have been found about these sequences. In the article [13], the authors obtained many features of these sequences with the Cholesky decomposition algorithm, using the 2 x 2 matrix belonging to a generalization of the Fibonacci sequence. In this study, it is shown that many different features can be found by using a 2 x 2 matrix belonging to the Lucas number sequence with the same method.