Explore the matrix representation of Discrete-Time Markov Chains (DTMC) in this 15-minute lecture. Delve into key concepts such as egodicity, ergodic chains, and ergodic classes. Learn about the global balance equation and its significance in DTMC analysis. Gain insights into n-step transition probabilities and their calculation using matrix notation. Enhance your understanding of stochastic processes and their mathematical foundations through this concise yet comprehensive presentation.