Introduction to Matrix Theory

This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

Dr. Arindama Singh is currently a Professor at the Department of Mathematics, Indian Institute of Technology Madras, India. He has 31 years of teaching and research experience. He has guided 5 Ph.D., 4 M.Phil., and 18 M.Sc. students. He has published 5 books, over 50 papers in refereed Journals, and 10 conference proceedings. He also has written some expository papers in basic mathematics. His areas of interest are the numerical solution of singularly perturbed differential equations (NSSPTPBVS), knowledge compilation, numerical solution of singularly perturbed elliptic problems (NSSPEP), image restoration, and mathematical learning theory.