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Matrix Functions and Matrix Equations by Zhaojun Bai Pdf
"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."--
Linear Algebra and Matrix Computations with MATLAB® by Dingyü Xue Pdf
This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.
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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.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.
This new edition of Matrix Methods emphasizes applications to Jordan-canonical forms, differential equations, and least squares. The revision now includes an entire new chapter on inner products, additional material on elementary row applications, and hundreds of new exercises.
Interpolation of Rational Matrix Functions by Joseph Ball,I. Gohberg,Rodman Pdf
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).
Linear Algebra and Matrix Computations with MATLAB by Dingyu Xue Pdf
The book focused on solving linear algebra practical problems with MATLAB. The input and manipulation of matrices are introduced first, followed by the matrix analysis and transformation problem solutions. Matrix equation solutions, matrix function evaluations, and various linear algebra applications are also demonstrated. With extensive exercises, the book sets up a new viewpoint for the readers in understanding linear algebra problems.
Author : Roger A. Horn,Charles R. Johnson Publisher : Cambridge University Press Page : 620 pages File Size : 48,8 Mb Release : 1994-06-24 Category : Mathematics ISBN : 9781107392953
Topics in Matrix Analysis by Roger A. Horn,Charles R. Johnson Pdf
Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics in matrix theory not included in the previous volume, but with important applications and of special mathematical interest. As with the previous volume, the authors assume a background knowledge of elementary linear algebra and rudimentary analytical concepts. Many examples and exercises of varying difficulty are included.
Author : Philip J. Davis Publisher : John Wiley & Sons Page : 376 pages File Size : 49,5 Mb Release : 1973 Category : Mathematics ISBN : CORNELL:31924010132722
Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.
Applied Matrix Algebra aims to develop an understanding of the Fundamentals of matrix algebra as well as the differential and integral calculus of matrices that are fundamental for the analysis of a wide range of applied problems. When used in conjunction with a matrix computational program, you will be in a position to readily analyze sophisticated and complex applied problems. Completion of the text should also prepare you for moving on to much more theoretical and advanced topics in linear algebra. You will understand not only the mathematical complexities of the subject, but also gain a greater insight into the intricate details of the computational algorithms with this helpful book.
This book contains a detailed guide to determinants and matrices in algebra. It offers an in-depth look into this area of mathematics, and it is highly recommended for those looking for an introduction to the subject. “Determinants and Matrices” is not to be missed by collectors of vintage mathematical literature. Contents include: “Linear Equations and Transformations”, “The Notation of Matrices”, “Matrices, Row and Column Vectors, Sealers”, “The Operations of Matrix Algebra”, “Matrix Pre- and Postmultiplication”, “Product of Three or More Matrices”, “Transposition of Rows and Columns”, “Transpose of a Product: Reversal Rule”, etc. Many vintage books such as this are becoming increasingly scarce and expensive. It is with this in mind that we are republishing this volume now in a modern, high-quality edition complete with the original text and artwork.
It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results--the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion. --Bulletin of the American Mathematical Society The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory. --Jahrbuch uber die Fortschritte der Mathematik In 1937, the theory of matrices was seventy-five years old. However, many results had only recently evolved from special cases to true general theorems. With the publication of his Colloquium Lectures, Wedderburn provided one of the first great syntheses of the subject. Much of the material in the early chapters is now familiar from textbooks on linear algebra. Wedderburn discusses topics such as vectors, bases, adjoints, eigenvalues and the characteristic polynomials, up to and including the properties of Hermitian and orthogonal matrices. Later chapters bring in special results on commuting families of matrices, functions of matrices--including elements of the differential and integral calculus sometimes known as matrix analysis, and transformations of bilinear forms. The final chapter treats associative algebras, culminating with the well-known Wedderburn-Artin theorem that simple algebras are necessarily isomorphic to matrix algebras. Wedderburn ends with an appendix of historical notes on the development of the theory of matrices, and a bibliography that emphasizes the history of the subject.
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
Author : G. S. Litvinchuk,I. M. Spitkovskii Publisher : Walter de Gruyter GmbH & Co KG Page : 376 pages File Size : 55,9 Mb Release : 2022-01-19 Category : Social Science ISBN : 9783112471722
Matrices and Transformations by Anthony J. Pettofrezzo Pdf
This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane is stressed. The purpose of this book is to familiarize the reader with the role of matrices in abstract algebraic systems, and to illustrate its effective use as a mathematical tool in geometry. The first two chapters cover the basic concepts of matrix algebra that are important in the study of physics, statistics, economics, engineering, and mathematics. Matrices are considered as elements of an algebra. The concept of a linear transformation of the plane and the use of matrices in discussing such transformations are illustrated in Chapter #. Some aspects of the algebra of transformations and its relation to the algebra of matrices are included here. The last chapter on eigenvalues and eigenvectors contains material usually not found in an introductory treatment of matrix algebra, including an application of the properties of eigenvalues and eigenvectors to the study of the conics. Considerable attention has been paid throughout to the formulation of precise definitions and statements of theorems. The proofs of most of the theorems are included in detail in this book. Matrices and Transformations assumes only that the reader has some understanding of the basic fundamentals of vector algebra. Pettofrezzo gives numerous illustrative examples, practical applications, and intuitive analogies. There are many instructive exercises with answers to the odd-numbered questions at the back. The exercises range from routine computations to proofs of theorems that extend the theory of the subject. Originally written for a series concerned with the mathematical training of teachers, and tested with hundreds of college students, this book can be used as a class or supplementary text for enrichments programs at the high school level, a one-semester college course, individual study, or for in-service programs.