An Eigenvalue Region for Leslie Matrices
Steve Kirkland · SIAM Journal on Matrix Analysis and Applications · 1992
Leslie matrices arise in a mathematical model for population growth and the eigenvalues of a Leslie matrix are important in describing the limiting behaviour of the corresponding population model. While it is well known that such matrices have exactly one positive eigenvalue, which dominates the others in modulus, little has been said about the nonpositive eigenvalues of a Leslie matrix, which are also of interest. In this paper, a brief description of the Leslie model is given, and a sharp containment region for the nonpositive spectrum of a Leslie matrix is constructed, characterizing the region in terms of some simple equations.