Matrix analysis

Author: (USA) Horn (Horn/R.A.) et al. / Yang Qi
Publisher:
Publish Date: 2005-04-01
Features: "There is no doubt that this book is a standard reference for numerical computation researchers." — ComputingReviews "Regardless of whether one is engaged in pure theoretical research in linear algebra or in its applied research, this book is an excellent reference." — SIAM Review "This book will undoubtedly become a standard textbook." — American Scientist "In conclusion, the authors have accomplished an outstanding work, providing a carefully organized and comprehensive overview of linear algebra and applied mathematics, which can serve as both a textbook and a reference. This book is an essential reference for everyone in the relevant fields." — American Scientist
Matrix theory, as a fundamental mathematical tool, is widely used in various fields of mathematics and other scientific and technological disciplines (such as numerical analysis, optimization theory, differential equations, probability and statistics, systems engineering, etc.). The development of electronic computers and computational technology has also opened up broader prospects for the application of matrix theory. Therefore, learning and mastering the basic theories and methods of matrix theory are essential for undergraduate and graduate students in science and engineering. This book integrates the two starting points of matrix analysis and discusses both the classical and modern results of matrix analysis. First, it includes topics in linear algebra that arise from the needs of mathematical analysis; second, it presents a method for solving real and complex linear algebra problems, decisively adopting concepts from analysis such as limits, continuity, and power series. Since its publication in 1985, this book has been praised and welcomed by an increasing number of mathematicians and scientists. To this day, it remains a highly valuable classic. Universities such as Tianjin University and Shanghai Jiao Tong University have adopted it as a textbook.
This book discusses classical and modern methods of matrix analysis from the perspective of mathematical analysis, with up-to-date content, a certain depth, and many important applications in multivariable calculus, complex analysis, differential equations, nonlinear optimization, and approximation theory. The main contents include: eigenvalues, eigenvectors, and similarity, unitary equivalence and normal matrices, canonical forms, Hermitian matrices and symmetric matrices, vector norms and matrix norms, eigenvalue estimation and perturbation, positive definite matrices, and nonnegative matrices. This book can serve as a graduate textbook for majors such as engineering, statistics, and economics, as well as a textbook for senior undergraduate students in mathematics, and can also be used as a reference for mathematicians and scientists.