Random Process and Linear Algebra is a comprehensive textbook that unifies two fundamental areas of mathematics and engineering, linear algebra and random processes, into a single cohesive resource. It provides a clear, structured, and application oriented approach that helps readers build both theoretical understanding and practical skills. The book covers essential concepts of linear algebra such as matrices, vector spaces, linear transformations, eigenvalues, and eigenvectors, along with an in depth study of random processes including probability theory, random variables, correlation, and stochastic modeling. Designed for students, educators, and professionals, it emphasizes conceptual clarity through step by step derivations, illustrative examples, and computational insights that connect mathematics to real world applications in fields such as data science, signal processing, and control systems. With its balanced combination of rigor and accessibility, this book serves as an ideal reference for learners seeking to master the principles of linear algebra and random processes while appreciating their importance in modern science, engineering, and technology.
About the Authors’
Dr. Md. Mushtaque Khan is presently serving as the University Professor and Head of the Department of Mathematics at Jai Prakash University, Chapra, Bihar. He is a distinguished scholar and an experienced academician in the field of Mathematics, contributing significantly to higher education for over two decades. Dr. Khan completed his B.Sc. and M.Sc. degrees in Mathematics from Tilka Manjhi Bhagalpur University, Bhagalpur. Later, he earned his Ph.D. in Mathematics from Bhupendra Narayan Mandal University, Madhepura. His profound interest in mathematical sciences and dedication to research have earned him high respect in academic circles. His areas of specialization include Mathematical Analysis, Algebra, and Applied Mathematics. He has published numerous research papers in national and international journals and actively guided several research scholars pursuing M.Phil. and Ph.D. degrees. Under his leadership, the Department of Mathematics at Jai Prakash University has made significant progress in academic and research activities. He is known for his disciplined approach, conceptual clarity, and encouragement of innovative thinking among students. Prof. Khan’s academic journey reflects a deep commitment to teaching, learning, and research. His continuous efforts have strengthened the foundation of mathematics education in Bihar and inspired a generation of students to pursue excellence in the subject.
Dr. Nasim Akhtar received his M.Sc. degree in Mathematics from Jai Prakash University, Chapra, Saran, Bihar, India, in 2008, securing a Gold Medal for his outstanding academic performance. Since 2010, He has been serving as a Senior Secondary Teacher in a government school, where he is dedicated to nurturing young minds and strengthening the foundation of Mathematics education. In recognition of his significant contributions to the field of education, he was honored with the State Teacher Award by the Government of Bihar in 2021.In 2025, He was awarded the degree of Doctor of Philosophy (Ph.D.) in Mathematics, specializing in Operations Research, from Jai Prakash University, Chapra, Saran, Bihar, India. His research focuses on developing efficient models and applications in the domains of Linear Programming, Optimization, Queueing Theory, and Decision-Making. Dr. Akhtar is also the author of several academic books at the secondary and senior secondary levels.
Mr. Manoj Kumar received his M.Sc. degree in Mathematics from Jai Prakash University, Chapra, Saran, Bihar, India, in 2010. He has been serving as a Senior Secondary Teacher in a government school since 2014, where he has been actively involved in teaching and academic development. Currently, He is pursuing research as a scholar in the field of Fuzzy Logic and its Applications in the Department of Mathematics, focusing on mathematical modeling and decision-making under uncertainty.
Dr. Jyoti Mishra is currently working as a Professor at Dept. Of Engineering Mathematics, Gyan Ganga Institute of Technology and Sciences, Jabalpur. She is a qualified individual with around 15 years of expertise in Teaching, R&D with specialization in Mathematics. She is B.Sc., M.Sc. & B.Ed. She received her Ph.D. degree in Special function from APS University, Rewa, India. She received her POSTDOC in Federal Institute of Science Education and Tech. of Ceara, Fortaleza, Brazil. Her research interests include Special function. Fractional Calculus, Partial differential Equations, special function, Mathematical Modeling. Been a part of various seminars, paper presentations, research paper reviews, conferences as co-convener, Member of Organizing Committee, Member of Advisory Committee, Member of Technical Committee. She has published more than 60 research papers in reputed journals such as SCI&SCIE, Elsevier, Springer, Scopus and UGC referred journal. She has been actively involved in professional bodies Indian Mathematical Society, IAPS, FATER. She is reviewer in many sci journals such as DCDCS, AIP, CHAOS, EPJP, and ELESVIER. She published 14 patents in Intellectual Property, India. She published 6 books.
Dr. Md. Naushad is a dedicated scholar in the field of Mathematics. He completed his Master of Science (M.Sc.) degree in Mathematics from Jai Prakash University, Chapra, Saran, Bihar, in 2010. His academic interests include Pure Mathematics, particularly Functional Analysis. Dr. Naushad is well known for his analytical thinking, commitment to teaching, and contributions to research activities. He regularly participates in academic seminars and workshops to enhance his knowledge. With a deep passion for education and innovation, he continues to inspire students and promote excellence in mathematical learning and research.
