Introduction to Matrix Theory
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Beschreibung
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.
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.
Covers topics such as elementary row operations and Gram–Schmidt orthogonalization, rank factorization, OR-factorization, Schurtriangularization, diagonalization of normal matrices, etc Includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix Contains exercises and problems at the end of each chapter
Autor*in
Arindama Singh
Themen in »Introduction to Matrix Theory«
Matrix Operations Linear Equations Orthogonality Eigenvalues Eigenvectors Canonical Forms Matrix norms Matrix as a Linear Map
Stimmen zu »Introduction to Matrix Theory«
“This is a concise, concrete introduction to matrix theory and linear algebra, designed as a one-semester course for science and engineering students. … The book has a reasonable number of exercises.” (Allen Stenger, MAA Reviews, December 12, 2021)
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