### 4.6.3 Properties of the Leslie matrix

The properties are:

1. there exists a unique positive value of say with the property that the corresponding eigenvector x0 can be thought of haa having only non-negative elements;
2. has the greatest absolute value of any eigenvalue in the system.

From a modelling point of view, Property 1 tells us that the Leslie model will always give a population distribution consisting of positive numbers only. This is important since it is impossible to consider populations with negative or complex numbers of animals! Property 1 also states that the age distribution is unique since is unique. Property 2 tells us that we can easily find the value of by finding the eigenvalue with the greatest absolute value. Packages such as Maple will find the complete eigensystem of a matrix so that it is easy to pick out the value of the eigenvalue and the corresponding eigenvector x0.