- 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; - has the greatest
absolute value of any eigenvalue in the system.
The properties are:
say with the property
that the corresponding eigenvector x0 can be thought
of haa having only non-negative elements; 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.