The set of conditions for a situation is defined as a state. The change from one state to another is called a transition.
Multiplying the transition matrix by the initial state matrix gives the present state. When you alter the power of the transition matrix, you can find the state for week 3 for instance by raising it to the power of 3.
If the values of your transition matrix are in percentage form between 0 and 1, the result will tend towards a certain value and stay there after a number of time periods. This is defined as the steady state matrix, and can be found by raising the transition matrix to a large value, or you can use an alternative method and evaluate the steady state matrix without the calculator lagging like crazy like this:
Where:
But the above method only works for a 2x2 Matrix.
Also another hint for when making transition matrices, the leading diagonal (values from the top left corner, diagonally towards the bottom right) of a transition matrix will generally always be larger because it shows what doesn't change.
Hope this has helped in some way.
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