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Books
Matrices
Coding the Matrix: Linear Algebra through Applications to Computer Science
Lowest new price: $31.11
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List price: $35.00
Author: Philip N Klein

An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: errorcorrecting codes, transformations in graphics, face detection, encryption and secretsharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be autograded online. Over two hundred illustrations, including a selection of relevant xkcd comics.
Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program
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Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences)
Lowest new price: $49.22
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List price: $70.00
Author: Gene H. Golub
Brand: Brand: Johns Hopkins University Press

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a covertocover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• largescale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrixsavvy developer of numerical methods and software.
Features:
 Used Book in Good Condition
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Matrix Analysis
Lowest new price: $41.98
Lowest used price: $42.94
List price: $55.00
Author: Roger A. Horn
Brand: Brand: Cambridge University Press

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as:  New sections on the singular value and CS decompositions  New applications of the Jordan canonical form  A new section on the Weyr canonical form  Expanded treatments of inverse problems and of block matrices  A central role for the Von Neumann trace theorem  A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetricskew symmetric pair  Expanded index with more than 3,500 entries for easy reference  More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finitedimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid  A new appendix provides a collection of problemsolving hints.
Features:
 Used Book in Good Condition
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Matrices and Linear Transformations: Second Edition (Dover Books on Mathematics)
Lowest new price: $9.12
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List price: $17.95
Author: Charles G. Cullen

"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine. This introductory textbook, aimed at sophomore and juniorlevel undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, indepth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.
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Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
Lowest new price: $57.20
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List price: $78.50
Author: J. B. Kuipers

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth centurya feat he celebrated by carving the founding equations into a stone bridgemathematicians 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 4tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9element) 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 stateoftheart applications. He presents a six degreeoffreedom 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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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Lowest new price: $38.99
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List price: $64.95
Author: Brian Hall

Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the oftenintimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.
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Fundamentals of Matrix Computations
Lowest new price: $97.95
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List price: $132.00
Author: David S. Watkins
Brand: Brand: Wiley

This new, modernized edition provides a clear and thorough introduction to matrix computations,a key component of scientific computing Retaining the accessible and handson style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. Along with new and updated examples, the Third Edition features:  A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm
 Application of classical GramSchmidt with reorthogonalization
 A revised approach to the derivation of the GolubReinsch SVD algorithm
 New coverage on solving product eigenvalue problems
 Expanded treatment of the JacobiDavidson method
 A new discussion on stopping criteria for iterative methods for solving linear equations
Throughout the book, numerous new and updated exercises—ranging from routine computations and verifications to challenging programming and proofs—are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve realworld problems in electrical circuits, massspring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software. Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upperundergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.
Features:
 Used Book in Good Condition
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Topics in Random Matrix Theory (Graduate Studies in Mathematics)
Lowest new price: $48.48
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List price: $64.00
Author: Terrence Tao

The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely selfcontained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
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HandsOn Matrix Algebra Using R: Active and Motivated Learning with Applications
Lowest new price: $52.22
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List price: $55.00
Author: Hrishikesh D Vinod
Brand: Brand: World Scientific Publishing Company

This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system. The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.
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Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics)
Lowest new price: $67.99
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List price: $99.00
Author: James E. Gentle

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This muchneeded work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
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