EIGENVALUE OF THE LESLIE MATRIX AND ITS APPLICATION TO FEMALE POPULATION GROWTH RATE IN BANYUMAS REGENCY

Abstrak

The Leslie matrix model is a method used to estimate the size and growth rate of the female population based on fertility and survival rates across age groups. This study aims to demonstrate the behavior of the dominant eigenvalue of the Leslie matrix and to apply it in estimating the growth rate of the female population in Banyumas Regency. The data used in this study consist of the female population in 2019 and 2024, as well as the number of female births during the period 2019–2024. The research stages include proving that the Leslie matrix has a unique positive eigenvalue, and that two consecutive entries in the first row of the Leslie matrix are nonzero. The subsequent stages involve determining age groups, calculating fertility and survival rates, constructing the Leslie matrix and the initial age distribution vector, and determining the dominant eigenvalue to estimate the growth rate of the female population in Banyumas Regency. The results show that the Leslie matrix has a single dominant positive eigenvalue. Furthermore, the dominant eigenvalue of the Leslie matrix in the female population growth model of Banyumas Regency is 0.991, indicating a decreasing trend in the growth rate of the female population every five years.