Markov chain is a mathematical model used to describe a system that transitions between different states over time. It is named after Russian mathematician Andrey Markov, who developed the theory in the early 20th century. A Markov chain consists of a set of states and a transition matrix, which specifies the probability of moving from one state to another. The probability of transitioning to a particular state depends only on the current state, and not on any previous history. This is known as the Markov property. The transition matrix is a square matrix where each row represents the probabilities of moving from one state to all other states. The sum of each row is equal to 1, since the system must transition to one of the possible states. Markov chains have many applications in various fields, including physics, economics, and computer science. They can be used to model a wide range of systems, such as weather patterns, stock market behavior, and text generation. In particular, Markov chains are often used in natural language processing to generate text that appears to be similar to a given input text, a technique known as Markov chain text generation.