I am currently working on a population dynamics model, in which I have to model the population growth of an animal with the survival rate and fecundity rate.
I have set-up a 6 x 6 Matrix below:
$$ \begin{pmatrix} 0 & 0 & 1.4 & 1.6 & 1.1 & 0.3 \\ 0.6 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0.6 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0.8 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0.3 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0.3 & 0 \\ \end{pmatrix} $$
Initial Population Matrix: $$ \begin{pmatrix} 1150\\ 1000\\ 975 \\ 750\\ 450\\ 200\\ \end{pmatrix} $$
I am struggling to calculate the eigenvalue/eigenvector and understand what exactly the eigenvalue/eigenvector indicates and what it can be used for.
Any help would be appreciated.