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# FM Equilibrium

## 2.1 Simple Matrix Recurrence Relations

### The Simple Matrix Recurrence Relation Formula

• The simplest type of matrix recurrence relation formula we will analyse in Further Maths models a system where the next “state”; S_{n+1}, can be reached by multiplying the current state; S_{n}, by a transition matrix; T, in the form:

S_{n+1}=T S_{n}

• The state matrices; S_{n} (where n is a positive whole number representing the state of the system), are column matrix listing the value of each of the system’s variables in the corresponding state.
• The transition matrix; T, is a square matrix.
• As with a linear recurrence relation, it is important to state the initial state of a system; S_{0}.
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