A Course in Linear Algebra

Designed for senior undergraduate and graduate courses in mathematics and engineering, this self-contained textbook discusses key topics in linear algebra with real-life applications. Split into two parts—theory in part I and solved problems in part II—the book makes both theoretical and applied linear algebra easily accessible. Topics such as sets and functions, vector spaces, linear transformations, eigenvalues and eigenvectors, normed spaces, and inner product spaces are discussed in part I; while in part II, over 500 meticulously solved problems show how to use linear algebra in real-life situations. A must-have book for linear algebra courses; it also serves as valuable supplementary material.

1.Preliminaries.- 2. Vector Spaces.- 3. Linear Transformations.- 4. Eigenvalues and Eigenvectors.- 5. Normed Spaces and Inner Product Spaces.- 6. Bounded Linear Maps.- 7. Solved Problems: Preliminaries.- 8. Solved Problems: Vector Spaces.- 9.Solved Problems: Linear Transformations.- 10.Solved Problems: Eigenvalues and Eigenvectors.- 11. Solved Problems: Normed Spaces and Inner Product Spaces.- 12.Solved Problems: Bounded Linear Maps.

Raju K. George is a professor at the Department of Mathematics and Dean (R&D) at the Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India. He earned his Ph.D. from the IIT Bombay, Maharashtra, India. He is a visiting faculty at the University of Delaware, USA, and he also has visited the University of Manitoba, Canada, and the University Paul Sabatier, France, for research purposes. Earlier, he was a faculty at MS University of Baroda and the University of Chemical Technology, Mumbai, India. His areas of research are the mathematical theory of control, machine learning, and computing and orbital dynamics.

Abhijith Ajayakumar is a research scholar at the Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India. He is currently working in the area of mathematical theory of control, mainly the controllability of networked control systems. He has completed his post-graduation from the University College (under the University of Kerala), Thiruvananthapuram, and under-graduation from Catholicate College (under Mahatma Gandhi University), Pathanamthitta, Kerala. He has a short working term as a guest lecturer at Catholicate College. His extended research interests include linear algebra.