Matrix Analysis

Author: Roger A. Horn,Roger A Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 9780521386326

Category: Mathematics

Page: 561

View: 5448

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Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.
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Topics in Matrix Analysis

Author: Roger A. Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 9780521467131

Category: Mathematics

Page: 607

View: 2680

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This book treats several topics in matrix theory not included in its predecessor volume, Matrix Analysis.
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Matrix Analysis

Author: Rajendra Bhatia

Publisher: Springer Science & Business Media

ISBN: 1461206537

Category: Mathematics

Page: 349

View: 1160

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This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
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Matrix Analysis

Author: Roger A. Horn,Charles R. Johnson

Publisher: Cambridge University Press

ISBN: 0521839408

Category: Business & Economics

Page: 643

View: 2841

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The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises.
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Introduction to Matrix Analysis

Second Edition

Author: Richard Bellman

Publisher: SIAM

ISBN: 0898713994

Category: Mathematics

Page: 403

View: 7538

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Lucid and concise, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods.
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Matrix Analysis and Applied Linear Algebra

Author: Carl D. Meyer

Publisher: SIAM

ISBN: 0898714540

Category: Mathematics

Page: 718

View: 4497

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This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.
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Matrix Analysis for Scientists and Engineers

Author: Alan J. Laub

Publisher: SIAM

ISBN: 9780898717907

Category: Mathematical analysis

Page: 157

View: 5149

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Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course. Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing.
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Numerical Matrix Analysis

Linear Systems and Least Squares

Author: Ilse C. F. Ipsen

Publisher: SIAM

ISBN: 0898716764

Category: Mathematics

Page: 128

View: 4765

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Matrix analysis presented in the context of numerical computation at a basic level.
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Linear Algebra and Matrix Analysis for Statistics

Author: Sudipto Banerjee,Anindya Roy

Publisher: CRC Press

ISBN: 1420095382

Category: Mathematics

Page: 580

View: 4625

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Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.
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Applied Linear Algebra and Matrix Analysis

Author: Thomas S. Shores

Publisher: Springer Science & Business Media

ISBN: 0387489479

Category: Mathematics

Page: 384

View: 8115

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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.
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