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Linear Algebra

  • M. Thamban Nair
  • Arindama Singh

Table of contents

  1. Front Matter
    Pages i-xi
  2. M. Thamban Nair, Arindama Singh
    Pages 1-50
  3. M. Thamban Nair, Arindama Singh
    Pages 51-105
  4. M. Thamban Nair, Arindama Singh
    Pages 107-161
  5. M. Thamban Nair, Arindama Singh
    Pages 163-208
  6. M. Thamban Nair, Arindama Singh
    Pages 209-242
  7. M. Thamban Nair, Arindama Singh
    Pages 243-275
  8. M. Thamban Nair, Arindama Singh
    Pages 277-334
  9. Back Matter
    Pages 335-341

About this book

Introduction

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 the end 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.

Keywords

Vector Spaces Linear Transformations Elementary Operations Inner Product Spaces Eigenvalues Block Diagonal Representation Spectral Decomposition

Authors and affiliations

  • M. Thamban Nair
    • 1
  • Arindama Singh
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

Bibliographic information