An absorbing state is a state from which there is a zero probability of exiting. An absorbing Markov system is a Markov system that contains at least one absorbing state, and is such that it is possible to get from each non-absorbing state to some absorbing state in one or more time-steps.

In analyzing an absorbing system, we number the states so that the absorbing states come last. The transition matrix $P$ of an absorbing system can be divided into four blocks as shown: Here:

1. $S$ is an $m \times m$ matrix representing the movement among the nonabsorbing states ($m ={}$ number of nonabsorbing states).
2. $I$ is the $n \times n$ identity matrix representing the only possible movement in the absorbing states ($n ={}$ number of absorbing states).
3. $T$ is the $m \times n$ matrix representing movement from nonabsorbing states to absorbing states.
4. $0$ is the zero $n \times m$ matrix representing the lack of movement from absorbing states to nonabsorbing states.

#[The fundamental matrix of such an asborbing system is the $n \times n$ matrix given by][La matriz fundamental de tal sistema absorbente es la matriz $n \times n$ que se da por]# #[Interpretation of $Q$ and $QT$][Interpretación de $Q$ y $QT$]#

• #[The $ij$ entry of $Q$ is the number of times, starting in state $i$, you expect to visit state $j$ before absorption. (If $i = j$ it is the number of times you expect to revisit state $i$ before absorption.)][La entrada $ij$ de $Q$ es el número de veces que, comenzando en el estado $i$, esperas visitar el estado $j$ antes de la absorción. (Si $i = j$ es el número de veces que esperas volver al estado $i$ antes de la absorción.)]#
• #[If you are currently in State $i$, the sum of the entries in the $i$th row of $Q$ is your "time to absorption": the number of time-steps it will take you to end up in an absorbing state.][Si actualmente te encuentras en el estado $i$, la suma de las entradas en la $i$ésima fila de $Q$ es tu "tiempo hasta la absorción": la cantidad de pasos de tiempo que le tomará terminar en un estado absorbente.]#
• #[The product $QT$ gives the probabilities of winding up in the different absorbing states depending on your current state. It the $i$th row of $QT$ is $[p_1\ \ p_2\ ... \ p_n]$, then starting in state $i$, there is a probability $p_1$ of winding up in the first absorbing state, a probability $p_2$ of winding up in the second absorbing state, and so on.][El producto $QT$ da las probabilidades de terminar en los diferentes estados absorbentes dependiendo de tu estado actual. Si la fila $i$ de $QT$ es $[p_1\ \ p_2\ ... \ p_n]$, entonces, comenzando en el estado $i$, hay una probabilidad $p_1$ de terminar en el primer estado absorbente, una probabilidad $p_2$ de terminar en el segundo estado absorbente, y así sucesivamente.]#