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Matrices
FiniteDimensional Vector Spaces
Lowest new price: $12.99
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Author: Paul Halmos

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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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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 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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Matrices: Algebra, Analysis And Applications
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Author: Shmuel Friedland

"People who do, or who plan to do, research in the topics in linear algebra that are covered here, will undoubtedly find this to be a very valuable book." Mathematical Association of America This volume deals with advanced topics in matrix theory using the notions and tools from algebra, analysis, geometry and numerical analysis. It consists of seven chapters that are loosely connected and interdependent. The choice of the topics is very personal and reflects the subjects that the author was actively working on in the last 40 years. Many results appear for the first time in the volume. Readers will encounter various properties of matrices with entries in integral domains, canonical forms for similarity, and notions of analytic, pointwise and rational similarity of matrices with entries which are locally analytic functions in one variable. This volume is also devoted to various properties of operators in inner product space, with tensor products and other concepts in multilinear algebra, and the theory of nonnegative matrices. It will be of great use to graduate students and researchers working in pure and applied mathematics, bioinformatics, computer science, engineering, operations research, physics and statistics.


Matrix Algebra: Theory, Computations, and Applications in Statistics (Springer Texts in Statistics)
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Author: James E. Gentle
Brand: Springer

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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Introduction to Modern Algebra and Matrix Theory: Second Edition (Dover Books on Mathematics)
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Author: O. Schreier
Brand: O Schreier

This unique text provides students with a singlevolume treatment of the basics of calculus and analytic geometry. It reflects the teaching methods and philosophy of Otto Schreier, an influential mathematician and professor. The order of its presentation promotes an intuitive approach to calculus, and it offers a strong emphasis on algebra with minimal prerequisites. Starting with affine space and linear equations, the text proceeds to considerations of Euclidean space and the theory of determinants, field theory and the fundamental theorem of algebra, elements of group theory, and linear transformations and matrices. Numerous exercises at the end of each section form important supplements to the text.
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 Introduction to Modern Algebra and Matrix Theory
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Matrix Analysis (Graduate Texts in Mathematics)
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Author: Rajendra Bhatia

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.


A Course in Metric Geometry
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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 CarnotCaratheodory metrics, the hyperbolic plane, distancevolume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (nonpositively and nonnegatively curved spaces). The authors tend to work with "easytotouch" mathematical objects using "easytovisualize" methods. The authors set a challenging goal of making the core parts of the book accessible to firstyear 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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 Used Book in Good Condition
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Matrix Algebra for Applied Economics
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Author: Shayle R. Searle
Brand: Shayle R Searle

Coverage of matrix algebra for economists and students of economics Matrix Algebra for Applied Economics explains the important tool of matrix algebra for students of economics and practicing economists. It includes examples that demonstrate the foundation operations of matrix algebra and illustrations of using the algebra for a variety of economic problems. The authors present the scope and basic definitions of matrices, their arithmetic and simple operations, and describe special matrices and their properties, including the analog of division. They provide indepth coverage of necessary theory and deal with concepts and operations for using matrices in reallife situations. They discuss linear dependence and independence, as well as rank, canonical forms, generalized inverses, eigenroots, and vectors. Topics of prime interest to economists are shown to be simplified using matrix algebra in linear equations, regression, linear models, linear programming, and Markov chains. Highlights include: * Numerous examples of realworld applications * Challenging exercises throughout the book * Mathematics understandable to readers of all backgrounds * Extensive uptodate reference material Matrix Algebra for Applied Economics provides excellent guidance for advanced undergraduate students and also graduate students. Practicing economists who want to sharpen their skills will find this book both practical and easytoread, no matter what their applied interests.
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 Matrix Algebra for Applied Economics


Matrix Algebra: Exercises and Solutions
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Author: David A. Harville
Brand: David A Harville

This book contains over 300 exercises and solutions that together cover a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small. This collection of exercises and their solutions will be a useful reference for students and researchers in matrix algebra. It will be of interest to mathematicians and statisticians.
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 Matrix Algebra Exercises and Solutions
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