## 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}.