\(
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\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
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\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Algebra
Markov matrices and their eigenvectors. An NZ-AU immigration example.
What is the population of Australia and New Zealand after 100 years of
the following migration pattern? Starting with 1 million people in Australia
and no one in New Zealand.
To start things off, the transition is described by:
[\[
\begin{bmatrix}
\text{Australia}_{t+1} \\
\text{New Zealand}_{t+1}
\end{bmatrix}
=
\begin{bmatrix}
? \, & ? \, \\
? \, & ? \,
\end{bmatrix}
\begin{bmatrix}
\text{Australia}_{t} \\
\text{New Zealand}_{t}
\end{bmatrix}
\] ]
Continue on the reverse. How does \( XVX^{-1} \) come up?
