This book introduces the fundamental concepts, techniques and results of linear algebra that form the basis of analysis, applied mathematics and algebra. Intended as a text for undergraduate students of mathematics, science and engineering with a knowledge of set theory, it discusses the concepts that are constantly used by scientists and engineers. It also lays the foundation for the language and framework for modern analysis and its applications.

Divided into seven chapters, it discusses vector spaces, linear transformations, best approximation in inner product spaces, eigenvalues and eigenvectors, block diagonalisation, triangularisation, Jordan form, singular value decomposition, polar decomposition, and many more topics that are relevant to applications. The topics chosen have become well-established over the years and are still very much in use. The approach is both geometric and algebraic. It avoids distraction from the main theme by deferring the exercises to theend of each section. These exercises aim at reinforcing the learned concepts rather than as exposing readers to the tricks involved in the computation. Problems included at the end of each chapter are relatively advanced and require a deep understanding and assimilation of the topics.

Autorentext

M. Thamban Nair is a professor of mathematics at the Indian Institute of Technology Madras, Chennai, India. He completed his Ph.D. at the Indian Institute of Technology Bombay, Mumbai, India, in 1986. His research interests include functional analysis and operator theory, specifically spectral approximation, the approximate solution of integral and operator equations, regularization of inverse and ill-posed problems. He has published three books, including a textbook, Functional Analysis: A First Course (PHI Learning), and a text-cum-monograph, Linear Operator Equations: Approximation and Regularization (World Scientific), and over 90 papers in reputed journals and refereed conference proceedings. He has guided six Ph.D. students and is an editorial board member of the Journal of Analysis and Number Theory, and Journal of Mathematical Analysis. He is a life member of academic bodies such as Indian Mathematical Society and Ramanujan Mathematical Society.

Arindama Singh is a professor of mathematics at the Indian Institute of Technology Madras, Chennai, India. He completed his Ph.D. at the Indian Institute of Technology Kanpur, India, in 1990. His research interests include knowledge compilation, singular perturbation, mathematical learning theory, image processing, and numerical linear algebra. He has published five books, including Elements of Computation Theory (Springer), and over 47 papers in reputed journals and refereed conference proceedings. He has guided five Ph.D. students and is a life member of many academic bodies, including Indian Society for Industrial and Applied Mathematics, Indian Society of Technical Education, Ramanujan Mathematical Society, Indian Mathematical Society, and The Association of Mathematics Teachers of India

Inhalt

Chapter 1. Vector Spaces.- Chapter 2. Linear Transformations.- Chapter 3. Elementary Operations.- Chapter 4. Inner Product Spaces.- Chapter 5. Eigenvalues and Eigenvectors.- Chapter 6. Block Diagonal Representation.- Chapter 7. Spectral Decomposition.