Answering Questions That Require Multiple Applications of a Transition Matrix (VCE SSCE General Mathematics): Flashcards

$S_0$, the starting situation before any transitions

Formula generating sequence of state matrices over time

$S_{n+1} = T \times S_n$ where $T$ is transition matrix

State matrix after $n$ applications of transition matrix

$S_1 = T \times S_0$

$S_n = T^n \times S_0$

For a few time steps (like 1, 2, or 3 periods)

For many time steps (like 20 or 40 periods)

When populations stabilise; equal movement in both directions

Movement continues but net effect is zero change