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Linear algebra is central to modern mathematics and underpins fields ranging from engineering and computer science to data science, machine learning, optimization, economics, and physics. This book was written to bridge the gap between computational proficiency and conceptual understanding by presenting rigorous mathematics in a clear, conversational, and highly engaging style.
Unlike many traditional texts that emphasize either abstract theory or routine computation, this book integrates motivation, intuitive explanations, geometric insight, formal proofs, historical notes, counterexamples, warnings, worked examples, and contemporary applications into a coherent learning experience. Every major concept is developed gradually, enabling readers to understand not only how linear algebra works but also why its ideas arise naturally and how they are interconnected. Carefully graded exercises, including concept checks, proofs, applications, challenging problems, and capstone exercises, support learners at every stage.
Suitable for undergraduate and beginning graduate students, the book also serves as a valuable reference for instructors, self-learners, and teachers seeking a classroom-friendly text. By combining accessibility with mathematical rigour, it provides a distinctive resource for readers ranging from first-time learners to advanced students and educators.
Dr. Pradip Debnath is an Associate Professor in the Department of Mathematical Sciences at Tezpur University, India. He has been recognised among the World’s Top 2% Scientists, as listed by Stanford University and published by Elsevier, for two consecutive years, 2023 and 2024. He served as a remunerative Associate Editor for the Mathematics section of Heliyon, an Elsevier/Cell Press journal, and is an active member of the editorial boards of several prestigious journals, including Scientific Reports (Nature Portfolio), Research in Mathematics (Taylor \& Francis), PLOS ONE, and the TWMS Journal of Applied and Engineering Mathematics, among others. Previously, Dr. Debnath held faculty positions as an Assistant Professor in the Department of Applied Science and Humanities at Assam University, Silchar (a central university in India), and in the Department of Mathematics at the North Eastern Regional Institute of Science and Technology (NERIST), India.
He earned his PhD in Mathematics from the National Institute of Technology Silchar, India. His primary research interests include fixed point theory, functional analysis, soft computing, and mathematical statistics. He has published over 80 research papers in internationally reputed journals and reviewed more than 500 manuscripts for over 82 international journals. He also reviews for Mathematical Reviews, published by the American Mathematical Society. As a lead editor/author, Dr. Debnath has published over 12 books with esteemed publishers such as Springer, CRC Press, De Gruyter and World Scientific. He actively collaborates with leading mathematicians from countries including Canada, Serbia, Portugal, South Korea, Thailand, Saudi Arabia, Iran, Spain, and Tunisia. Additionally, he is a Topical Advisory Panel Member for the journals Axioms and Fractal and Fractional. He has served as a Guest Editor for several special issues across different journals, including Research in Mathematics, Symmetry, Axioms, and Contemporary Mathematics. He has successfully supervised PhD students in nonlinear analysis, soft computing, and fixed point theory. He has completed a major Basic Science Research Project in fixed point theory funded by the University Grants Commission (UGC), Government of India. An academic gold medalist during his postgraduate studies at Assam University, Silchar, Dr. Debnath has also qualified for several national-level mathematics examinations in India.