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Functions Of Matrices


Functions Of Matrices
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Functions Of Matrices


Functions Of Matrices
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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2008-01-01

Functions Of Matrices written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.


A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.



Matrix Functions And Matrix Equations


Matrix Functions And Matrix Equations
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Author : Zhaojun Bai
language : en
Publisher: World Scientific
Release Date : 2015-09-04

Matrix Functions And Matrix Equations written by Zhaojun Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-04 with Mathematics categories.


Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects.



Introduction To Matrix Analysis And Applications


Introduction To Matrix Analysis And Applications
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Author : Fumio Hiai
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-06

Introduction To Matrix Analysis And Applications written by Fumio Hiai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-06 with Mathematics categories.


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.



Hierarchical Matrices Algorithms And Analysis


Hierarchical Matrices Algorithms And Analysis
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2015-12-21

Hierarchical Matrices Algorithms And Analysis written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-21 with Mathematics categories.


This self-contained monograph presents matrix algorithms and their analysis. The new technique enables not only the solution of linear systems but also the approximation of matrix functions, e.g., the matrix exponential. Other applications include the solution of matrix equations, e.g., the Lyapunov or Riccati equation. The required mathematical background can be found in the appendix. The numerical treatment of fully populated large-scale matrices is usually rather costly. However, the technique of hierarchical matrices makes it possible to store matrices and to perform matrix operations approximately with almost linear cost and a controllable degree of approximation error. For important classes of matrices, the computational cost increases only logarithmically with the approximation error. The operations provided include the matrix inversion and LU decomposition. Since large-scale linear algebra problems are standard in scientific computing, the subject of hierarchical matrices is of interest to scientists in computational mathematics, physics, chemistry and engineering.



Operator Theory Analytic Functions Matrices And Electrical Engineering


Operator Theory Analytic Functions Matrices And Electrical Engineering
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Author : J. William Helton
language : en
Publisher: American Mathematical Soc.
Release Date : 1987

Operator Theory Analytic Functions Matrices And Electrical Engineering written by J. William Helton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.


Expands the lectures given at a regional conference in Lincoln, Nebraska which brought together a wide variety of scientists, pure mathematicians and engineers.



Introduction To Applied Linear Algebra


Introduction To Applied Linear Algebra
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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07

Introduction To Applied Linear Algebra written by Stephen Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-07 with Business & Economics categories.


A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.



Functions Of Matrices


Functions Of Matrices
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Author : Nicholas J. Higham
language : en
Publisher:
Release Date : 2008

Functions Of Matrices written by Nicholas J. Higham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Factorization (Mathematics) categories.


A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.



Matrix Theory


Matrix Theory
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Author : Fuzhen Zhang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Matrix Theory written by Fuzhen Zhang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.


The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains eight chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The book can be used as a text or a supplement for a linear algebra and matrix theory class or seminar for senior or graduate students. The only prerequisites are a decent background in elementary linear algebra and calculus. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields.



Eigenvalues Of Matrices


Eigenvalues Of Matrices
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Author : Francoise Chatelin
language : en
Publisher: SIAM
Release Date : 2013-01-03

Eigenvalues Of Matrices written by Francoise Chatelin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-03 with Mathematics categories.


A comprehensive and accessible guide to the calculation of eigenvalues of matrices, ideal for undergraduates, or researchers/engineers in industry.



Square Matrices Of Order 2


Square Matrices Of Order 2
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Author : Vasile Pop
language : en
Publisher: Springer
Release Date : 2017-04-04

Square Matrices Of Order 2 written by Vasile Pop and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-04 with Mathematics categories.


This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding advanced topics. They will follow every notion of matrix theory with ease, accumulating a thorough understanding of algebraic and geometric aspects of matrices of order 2. The prime jewel of this book is its offering of an unusual collection of problems, theoretically motivated, most of which are new, original, and seeing the light of publication for the first time in the literature. Nearly all of the exercises are presented with detailed solutions and vary in difficulty from easy to more advanced. Many problems are particularly challenging. These, and not only these, invite the reader to unleash their creativity and research capabilities and to discover their own methods of attacking a problem. Matrices have a vast practical importance to mathematics, science, and engineering; therefore the readership of this book is intended to be broad: high school students wishing to learn the fundamentals of matrix theory, first year students who like to participate in mathematical competitions, graduate students who want to learn more about an application of a certain technique, doctoral students who are preparing for their prelim exams in linear algebra, and linear algebra instructors. Chapters 1–3 complement a standard linear algebra course. Pure and applied mathematicians who use matrix theory for their applications will find this book useful as a refresher. In fact, anyone who is willing to explore the methodologies discussed in this book and work through a collection of problems involving matrices of order 2 will be enriched.