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Books
Matrices
266 Solutions to Problems from Linear Algebra 4th ed., Friedberg, Insel, Spence
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Author: Daniel Callahan

Linear Algebra 4th ed., by Friedberg, Insel, and Spence is one of the world's best textbooks on the subject of finitedimensional linear analysis. This book offers 266 solutions to problems from chapters 17. Specifically, there are 27 solutions to problems in chapter 1; 64 solutions to problems in chapter 2; 17 solutions to problems in chapter 3; 16 solutions to problems in chapter 4; 44 solutions to problems in chapter 5; 50 solutions to problems in chapter 6; and 8 solutions to problems in chapter 7.
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Totally Positive Matrices (Cambridge Tracts in Mathematics)
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Author: Allan Pinkus
Brand: Allan Pinkus

Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin. This monograph will appeal to those with an interest in matrix theory, to those who use or have used total positivity, and to anyone who wishes to learn about this rich and interesting subject.
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 Totally Positive Matrices


Topics in Random Matrix Theory (Graduate Studies in Mathematics)
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Author: Terence 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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Matrix Analysis for Statistics (Wiley Series in Probability and Statistics)
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Author: James R. Schott

An uptodate version of the complete, selfcontained introduction to matrix analysis theory and practice Providing accessible and indepth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easytofollow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the stepbystep process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the MoorePenrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: • New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors • Additional problems and chapterend practice exercises at the end of each chapter • Extensive examples that are familiar and easy to understand • Selfcontained chapters for flexibility in topic choice • Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upperundergraduate and graduatelevel courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.
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Matrix Analysis for Scientists and Engineers
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Author: Alan J. Laub
Brand: Brand: SIAM: Society for Industrial and Applied Mathematics

Matrix Analysis for Scientists and Engineers provides a blend of undergraduate and graduatelevel 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 oftenneeded bridge between undergraduatelevel matrix theory and linear algebra and the level of matrix analysis required for graduatelevel study and research. The text is sufficiently compact that the material can be taught comfortably in a onequarter or onesemester 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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 Used Book in Good Condition
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Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms)
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Author: Timothy A. Davis

Fundamentals of Algorithms 2 Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an indepth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages. With a strong emphasis on MATLAB® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations. This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing. Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fillreducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index. "Overall, the book is magnificent. It fills a longfelt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent.." John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.
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Matrix Algebra: An Introduction (Quantitative Applications in the Social Sciences)
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Author: Krishnan Namboodiri
Brand: Brand: SAGE Publications, Inc

Matrix Algebra is a vital tool for mathematics in the social sciences, and yet many social scientists have only a rudimentary grasp of it. This volume serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. Namboodiri′s presentation is smooth and readable: it begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors  supplying illustrations through fullyworked examples.
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 Used Book in Good Condition
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Eigenvalue Distribution of Large Random Matrices (Mathematical Surveys and Monographs)
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Author: Leonid Pastur

Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by wellknown experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and selfcontained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
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FiniteDimensional Vector Spaces
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Author: Paul Halmos
Brand: Halmos Paul

Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes "My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets ...". This text is an ideal supplement to modern treatments of Linear Algebra. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." Zentralblatt für Mathematik.
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 Finite Dimensional Vector Spaces
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Topics in Matrix Analysis
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Author: Roger A. Horn
Brand: Brand: Cambridge University Press

Building on the foundations of its predecessor volume, Matrix Analysis, this book treats in detail several topics with important applications and of special mathematical interest in matrix theory not included in the previous text. These topics include the field of values, stable matrices and inertia, singular values, matrix equations and Kronecker products, Hadamard products, and matrices and functions. The authors assume a background in elementary linear algebra and knowledge of rudimentary analytical concepts. The book should be welcomed by graduate students and researchers in a variety of mathematical fields both as an advanced text and as a modern reference work.
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