A matrix is introduced to provide an efficient algebraic process for moving from one state vector to later state vectors, such as S2 or S100, rather than re-reading the diagram each time.
Conditions: The Markov chain has fixed one-step transition probabilities.; State vectors are represented in a consistent order.
A matrix is introduced to provide an efficient algebraic process for moving from one state vector to later state vectors, such as S2 or S100, rather than re-reading the diagram each time.
Conditions: The Markov chain has fixed one-step transition probabilities.; State vectors are represented in a consistent order.
Matrices and vectors are introduced as a linear algebra formalism to make manipulations and calculations simpler when studying a Markov chain, especially for iterating states efficiently over many steps.
Conditions: The problem involves a Markov chain.; The goal is to compute future states or manipulate transition probabilities.
Matrices and vectors are introduced as a linear algebra formalism to make manipulations and calculations simpler when studying a Markov chain, especially for iterating states efficiently over many steps.
Conditions: The problem involves a Markov chain.; The goal is to compute future states or manipulate transition probabilities.
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.