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No, $S_0 = (1,0)^T$ is not the only possible initial state. It is an asserted initial condition for this specific example.

Conditions: The system is a Markov chain with states A and B.; The entries of the initial state vector are probabilities.; The sum of the probabilities in the initial state vector must equal 1.

No, $S_0 = (1,0)^T$ is not the only possible initial state. It is an asserted initial condition for this specific example.

Conditions: The system is a Markov chain with states A and B.; The entries of the initial state vector are probabilities.; The sum of the probabilities in the initial state vector must equal 1.

The initial state vector $S_0$ is a column vector that encodes the starting probabilities of the Markov chain. In this specific example, $S_0 = (1, 0)^T$, meaning the system starts in state A with probability 1 and in state B with probability 0.

Conditions: The system has two states, A and B.; The components are ordered consistently with the states, here A then B.; The entries are probabilities describing the initial distribution.

The initial state vector $S_0$ is a column vector that encodes the starting probabilities of the Markov chain. In this specific example, $S_0 = (1, 0)^T$, meaning the system starts in state A with probability 1 and in state B with probability 0.

Conditions: The system has two states, A and B.; The components are ordered consistently with the states, here A then B.; The entries are probabilities describing the initial distribution.

In the two-state example, the first (top) component of the state vector corresponds to state A, and the second (bottom) component corresponds to state B. If there were more states, such as A, B, and C, the vector would have three components.

Conditions: The system is represented by a state vector.; The ordering of states is fixed.

In the two-state example, the first (top) component of the state vector corresponds to state A, and the second (bottom) component corresponds to state B. If there were more states, such as A, B, and C, the vector would have three components.

Conditions: The system is represented by a state vector.; The ordering of states is fixed.