Transition Matrices – Using Recursion (VCE SSCE General Mathematics): Quizzes

$S_{n+1} = T S_n$

$S_n = T^n S_0$

The transition matrix $T$

$S_n = T^{-1} S_{n+1}$

Elements may be negative or >1

When values stabilize and stop changing

Regular matrix; columns sum to 1

Flows balanced; inflows equal outflows

Check successive states agree

For large values of $n$