Transition Matrix and Markov Chains

Now, we will be looking at one of the applications of matrices, which is a field of study all by itself. Markov chains make use of transition matrices, probability, and limits to solve real-world problems. The real world is rarely as perfect as the mathematical models we create to solve them. A car may want to travel from point A to B, but distance and speed prove insufficient parameters in reality. A cat crossing the street may completely alter all the calculations that were made to calculate the time traveled by the car. A stock market may seem to be following a predictable pattern for a few days, but overnight, an event occurs that completely crashes it. That event may be some global event, a political statement, or the release of company reports. Of course, our development in mathematical and computational models has still not reached the place where we can predict the outcome of each of these events, but we can try and determine the probability...