Introduction to Matrix Analysis and Applications PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introduction to Matrix Analysis and Applications PDF full book. Access full book title Introduction to Matrix Analysis and Applications by Fumio Hiai. Download full books in PDF and EPUB format.
Author: Fumio Hiai
Publisher: Springer Science & Business Media
ISBN: 3319041509
Category : Mathematics
Languages : en
Pages : 337
Get Book Here
Book Description
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Author: Fumio Hiai
Publisher: Springer Science & Business Media
ISBN: 3319041509
Category : Mathematics
Languages : en
Pages : 337
Get Book Here
Book Description
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Author: Xian-Da Zhang
Publisher: Cambridge University Press
ISBN: 1108417418
Category : Computers
Languages : en
Pages : 761
Get Book Here
Book Description
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
Author: Edward Barry Saff
Publisher: John Wiley & Sons
ISBN: 1118953657
Category : Mathematics
Languages : en
Pages : 407
Get Book Here
Book Description
An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.
Author: Mohamed Ali Karim
Publisher:
ISBN: 9781681171876
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Matrix analysis is the study of matrices and their algebraic properties. Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices), and the eigenvalues of matrices (eigendecomposition of a matrix, eigenvalue perturbation theory). Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis. The book treats some aspects of analysis related to matrices including such topics as matrix monotone functions, matrix means, majorization, entropies, quantum Markov triplets. There are several popular matrix applications for quantum theory. This book emphasizes on these aspects of matrix analysis from an efficient analysis point of view. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Author: Richard Bellman
Publisher: SIAM
ISBN: 0898713994
Category : Mathematics
Languages : en
Pages : 424
Get Book Here
Book Description
Lucid and concise, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods.
Author: Thomas S. Shores
Publisher: Springer Science & Business Media
ISBN: 0387489479
Category : Mathematics
Languages : en
Pages : 394
Get Book Here
Book Description
This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.
Author: Arindama Singh
Publisher: Springer Nature
ISBN: 303080481X
Category : Mathematics
Languages : en
Pages : 199
Get Book Here
Book Description
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.
Author: Ferenc Szidarovszky
Publisher: World Scientific
ISBN: 9789810245139
Category : Business & Economics
Languages : en
Pages : 516
Get Book Here
Book Description
In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.
Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477
Get Book Here
Book Description
A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.
Author: Denis Serre
Publisher: Springer Science & Business Media
ISBN: 1441976833
Category : Mathematics
Languages : en
Pages : 291
Get Book Here
Book Description
In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.
