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.
General
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