Introduction to Matrix Theory - Arindama Singh

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Résumé :
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.

Biographie:
Dr. Arindama Singh is a professor in the Department of Mathematics, Indian Institute of Technology (IIT) Madras, India. He received his Ph.D. degree from the IIT Kanpur, India, in 1990. His research interests include knowledge compilation, singular perturbation, mathematical learning theory, image processing, and numerical linear algebra. He has published six books, over 60 papers in journals and conferences of international repute. He has guided ?ve Ph.D. students and is a life member of many academic bodies, including the 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....

Sommaire:
Matrix Operations.- Systems of Linear Equations.- Matrix as a Linear Map.- Orthogonality.- Eigenvalues and Eigenvectors.- Canonical Forms.- Norms of Matrices.- Short Bibliography.- Index.