Markov Chains Through Linear Algebra
A Matrix-Based Approach to Understanding Stochastic Processes
What if the seemingly random events around you—from weather patterns to stock market fluctuations—actually follow predictable mathematical rules that can be decoded using matrices and linear transformations? This comprehensive guide bridges the gap between abstract probability theory and concrete linear algebra applications, showing you how Markov chains emerge naturally from matrix operations. You'll discover how transition matrices encode the complete behavior of stochastic systems, and learn to predict long-term outcomes using eigenvalues and eigenvectors. Through carefully crafted examples and step-by-step derivations, you'll master the art of modeling real-world phenomena as Markov processes. Whether you're analyzing random walks, understanding absorption probabilities, or exploring the mathematics behind Google's PageRank algorithm, this book provides the linear algebra toolkit you need. You'll learn to classify states, compute steady-state distributions, and determine convergence properties—all through the lens of matrix theory. By the end, you'll possess a deep understanding of how linear algebra illuminates the hidden structure within seemingly chaotic systems, giving you powerful analytical tools for tackling complex probabilistic problems across science, engineering, and beyond.
Est. Length
253 pages (13 chapters)
Language
English
Publication date
Oct 15, 2025
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