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Matrix Theory: Basic Results and Techniques (Universitext)

Matrix Theory: Basic Results and Techniques (Universitext) Lowest new price: $64.87
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Author: Fuzhen Zhang
Brand: Brand: Springer New York

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students.  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.

Major changes in this revised and expanded second edition:
-Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms 
-A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices
-A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.


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A Course in Metric Geometry

A Course in Metric Geometry Lowest new price: $52.98
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Author: Dmitri Burago
Brand: Brand: American Mathematical Society

"Metric geometry" is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations. The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Caratheodory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with "easy-to-touch" mathematical objects using "easy-to-visualize" methods. The authors set a challenging goal of making the core parts of the book accessible to first-year graduate students. Most new concepts and methods are introduced and illustrated using simplest cases and avoiding technicalities. The book contains many exercises, which form a vital part of exposition.


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Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics and Scientific Computation)

Krylov Subspace Methods: Principles and Analysis (Numerical Mathematics and Scientific Computation) Lowest new price: $109.92
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Author: Jorg Liesen
Brand: Brand: Oxford University Press

The mathematical theory of Krylov subspace methods with a focus on solving systems of linear algebraic equations is given a detailed treatment in this principles-based book. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss-Christoffel quadrature, continued fractions, and, more generally, of Vorobyev's method of moments. Using the concept of cyclic invariant subspaces, conditions are studied that allow the generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the important practical distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples.

There is an emphasis on the way algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation and computation cannot be separated from each other. The book also underlines the importance of the historical context and demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are included as an inherent part of the text as well as the formulation of some omitted issues and challenges which need to be addressed in future work.

This book is applicable to a wide variety of graduate courses on Krylov subspace methods and related subjects, as well as benefiting those interested in the history of mathematics.


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Matrix Population Models

Matrix Population Models Lowest new price: $200.00
Lowest used price: $180.02
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Author: Hal Caswell
Brand: Brand: Sinauer Associates

Matrix Population Models, Second Edition, is a comprehensive treatment of matrix population models and their applications in ecology and demography. It begins with simple cases, presented in detail so that beginning students can learn how to use these powerful models. It goes on to cover advanced topics in stochastic and nonlinear models. Analytical methods and theoretical issues are illustrated with empirical examples throughout. The decade since the publication of the First Edition of this book has seen enormous progress in the theory and application of matrix population models. The new edition includes greatly expanded treatment of stochastic and density-dependent models, sensitivity analysis, and statistical inference, and new chapters on parameter estimation, structured population models, demographic stochasticity, and applications of matrix models in conservation biology. Matrix Population Models, Second Edition, is an indispensable reference for graduate students and researchers in ecology, population biology, conservation biology, and human demography.


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Handbook of Matrices

Handbook of Matrices Lowest new price: $120.24
Lowest used price: $90.00
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Author: Helmut Lütkepohl
Brand: Helmut Lutkepohl

Matrices are used in many fields such as statistics, econometrics, mathematics, natural sciences and engineering. They provide a concise, simple method for describing long and complicated computations. This is a comprehensive handbook and dictionary of terms for matrix theory.


  • Handbook of Matrices

Schaum's Outline of Theory and Problems of Matrix Operations

Schaum's Outline of Theory and Problems of Matrix Operations Lowest new price: $12.00
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Author: Richard Bronson
Brand: Richard Bronson

Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's.

More than 40 million students have trusted Schaum's Outlines to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. In Schaum's foreign language outlines, you'll get hundreds of examples, helpful usage explanations, and practice exercises to test your skills.

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.


  • ISBN13: 9780070079786
  • Condition: New
  • Notes: BRAND NEW FROM PUBLISHER! 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!

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Special Matrices and Their Applications in Numerical Mathematics: Second Edition (Dover Books on Mathematics)

Special Matrices and Their Applications in Numerical Mathematics: Second Edition (Dover Books on Mathematics) Lowest new price: $12.24
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Author: Miroslav Fiedler

This revised and corrected second edition of a classic book on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference.
Author Miroslav Fiedler, a Professor at the Institute of Computer Science of the Academy of Sciences of the Czech Republic, Prague, begins with definitions of basic concepts of the theory of matrices and fundamental theorems. In subsequent chapters, he explores symmetric and Hermitian matrices, the mutual connections between graphs and matrices, and the theory of entrywise nonnegative matrices. After introducing M-matrices, or matrices of class K, Professor Fiedler discusses important properties of tensor products of matrices and compound matrices and describes the matricial representation of polynomials. He further defines band matrices and norms of vectors and matrices. The final five chapters treat selected numerical methods for solving problems from the field of linear algebra, using the concepts and results explained in the preceding chapters.

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Quaternions and Rotation Sequences

Quaternions and Rotation Sequences Lowest new price: $128.79
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Author: J. B. Kuipers
Brand: Princeton University Press

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.

The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.


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Matrix Theory and Applications with MATLAB

Matrix Theory and Applications with MATLAB Lowest new price: $33.84
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Author: Darald J. Hartfiel
Brand: Brand: CRC Press

Designed for use in a second course on linear algebra, Matrix Theory and Applications with MATLAB covers the basics of the subject-from a review of matrix algebra through vector spaces to matrix calculus and unitary similarity-in a presentation that stresses insight, understanding, and applications. Among its most outstanding features is the integration of MATLAB throughout the text. Each chapter includes a MATLAB subsection that discusses the various commands used to do the computations in that section and offers code for the graphics and some algorithms used in the text.

All of the material is presented from a matrix point of view with enough rigor for students to learn to compose arguments and proofs and adjust the material to cover other problems. The treatment includes optional subsections covering applications, and the final chapters move beyond basic matrix theory to discuss more advanced topics, such as decompositions, positive definite matrices, graphics, and topology.

Filled with illustrations, examples, and exercises that reinforce understanding, Matrix Theory and Applications with MATLAB allows readers to experiment and visualize results in a way that no other text does. Its rigor, use of MATLAB, and focus on applications better prepares them to use the material in their future work and research, to extend the material, and perhaps obtain new results of their own.


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Matrix Analysis and Applications

Matrix Analysis and Applications Lowest new price: $74.81
Lowest used price: $769.70
List price: $74.99
Author: Xian-Da Zhang

This balanced and comprehensive study presents the theory, methods and applications of matrix analysis in a new theoretical framework, allowing readers to understand second-order and higher-order matrix analysis in a completely new light. Alongside the core subjects in matrix analysis, such as singular value analysis, the solution of matrix equations and eigenanalysis, the author introduces new applications and perspectives that are unique to this book. The very topical subjects of gradient analysis and optimization play a central role here. Also included are subspace analysis, projection analysis and tensor analysis, subjects which are often neglected in other books. Having provided a solid foundation to the subject, the author goes on to place particular emphasis on the many applications matrix analysis has in science and engineering, making this book suitable for scientists, engineers and graduate students alike.

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