Mathematical Properties of n x n Nonnegative Matrix Case of Irreducible Leslie Matrix
*Ema Carnia, Nursanti Anggriani, Maya Gustyana & Asep K. Supriatna

Department of Mathematics, Padjadjaran University, Jl. Raya Bandung-Sumedang Km 21, Jatinangor 45363, Indonesia

Abstract

Perron-Frobenius theorem describe five properties of irreducible nonnegative matrix. Leslie matrix is one of nonnegative matrix. Leslie matrix that used in this research is limited to the irreducible Leslie matrix. In previous research has been proven that irreducible Leslie matrix satisfies three properties in Perron-Frobenius theorem by spectral radius. This research completed the previous research, proving that irreducible Leslie matrix has a unique Perron vector and satisfies Collatz Wielandt formula. Leslie matrix is a primitive matrix. It is used to calculate the number of population in the future. Growth of population is interpreted by value spectral radius of Leslie matrix.

Keywords: Leslie matrix, positive matrix, Peron Frobenius

Topic: Mathematics