Random Processes and Linear Algebra is a comprehensive academic text designed to provide a systematic understanding of two important areas of applied mathematics essential to engineering, science, computing, and technology. The book develops the fundamental concepts of random processes and their mathematical representation for analyzing phenomena that evolve with time under conditions of uncertainty. It provides a structured treatment of random processes, including their classification, statistical characteristics, and important probabilistic measures. The discussion progresses to strictly stationary processes, emphasizing time-invariant statistical properties and their significance in mathematical and engineering analysis. Second-order and wide-sense stationary processes are developed with appropriate emphasis on correlation and covariance concepts. The book also covers ergodic processes and their role in relating time averages to ensemble averages. Markov processes and Poisson processes are introduced to develop an understanding of stochastic systems and continuous-time probabilistic models. Discrete-parameter Markov processes, or Markov chains, are treated systematically to strengthen the study of state-transition models and stochastic behavior. The second major component of the book presents the fundamental principles of linear algebra through vectors, matrices, vector spaces, and related algebraic structures. It provides detailed coverage of subspaces, linear combinations, systems of linear equations, linear dependence and independence, bases, and dimension. The presentation maintains a balance between theoretical foundations and practical mathematical understanding through definitions, properties, illustrative examples, and systematic problem-solving approaches. The integrated treatment of random processes and linear algebra highlights their importance in communication systems, signal processing, control systems, data science, artificial intelligence, and other modern technological applications. With its organized chapter structure and progressive development of concepts, the book is suitable for undergraduate students, teachers, researchers, and professionals seeking a reliable reference for mathematical analysis and applications.
About the Authors’
Dr. D. Saraswathi is an Assistant Professor in the Department of Mathematics at M.I.E.T. Engineering College, Tamil Nadu. She is dedicated to mathematics education and research, with interests in applied mathematics, engineering mathematics, and student-centered learning, contributing actively to academic excellence and scholarly development.
Dr. R. Yogarani is an Assistant Professor in the Department of Mathematics at M. S. S. Wakf Board College, Madurai. She has extensive experience in mathematics teaching and is committed to fostering analytical thinking, research aptitude, and academic growth among students through innovative pedagogical practices.
Dr. A.P.Pushpalatha received her Master’s degree in Mathematics in 1995 and her Ph.D. degree in 2011 from Madurai Kamaraj University, Madurai, India. She is currently a Professor and Head of the Mathematics Department at Velammal College of Engineering and Technology, Madurai, India. With 29 years of teaching experience and 20 years of research experience, Dr. Pushpalatha is renowned for being an excellent teacher and academician. She has published nearly 35 research articles and received the IJRULA Best Researcher award in 2018. Additionally, she serves as a reviewer for journals such as Advances and Applications in Mathematical Sciences and Discrete Mathematics, Algorithms, and Applications. Her research interests include graph theory, networking, discrete mathematics, and fuzzy graphs.
Mr. A. Durai Ganesh is an Assistant Professor in the Department of Mathematics at PET Engineering College, Tamil Nadu. He is committed to excellence in mathematics education, inspiring students through innovative teaching, analytical thinking, and problem-solving approaches while actively contributing to academic development and scholarly pursuits in the field of mathematics.
Dr. A. Manshath is an Assistant Professor (Senior Grade) in the Department of Mathematics and Actuarial Science at B. S. Abdur Rahman Crescent Institute of Science and Technology. His academic interests include actuarial science, applied mathematics, and statistical modeling. He actively contributes to teaching, research, and interdisciplinary academic initiatives, fostering excellence in higher education.
