Book Description

The statistical models confronting econometricians are complicated in nature so it is no easy task to apply the procedures recommended by classical statisticians to such models. This book presents the reader with mathematical tools drawn from matrix calculus and zero-one matrices and demonstrates how the use of their tools greatly facilitates such applications in a sequence of linear econometric models of increasing statistical complexity.The book differs from others in that the matrix calculus results are derived from a few basic rules which are generalizations of the rules used in ordinary calculus.Moreover the properties of several new zero-one matrices are investigated. ... Read more

Book Description

Packed with plenty of clear illustrations, this introductory work shows how to use the matrix methods of structural analysis to predict the static response of structures. Sack emphasizes the stiffness method while providing balanced coverage of the fundamentals of the flexibility method as well. He introduces the various topics in a logical series and develops equations from basic concepts. The result: readers will gain a firm grasp of theory as well as practical applications. Practical in approach, the well- presented material in this volume is devoted to giving a solid understanding of matrix analysis methods combined with the background to write computer programs and use production-level programs to build actual structures. ... Read more

Reviews (1)

Short but well stuffed
It is a very good, albeit succinct, reference on the direct stiffness method. Very useful for review or a quick reference. I used it as pocket TA during Prof. Filippou CE 220 course, even if the course covered a wider range of topics. ... Read more

Book Description

This book presents the authors' personal selection of topics in multivariate statistical analysis with emphasis on tools and techniques. Topics included range from definitions of multivariate moments, multivariate distributions, asymptotic distributions of commonly used statistics and density approximations to a modern treatment of multivariate linear models. The theory used is based on matrix algebra and linear spaces and applies lattice theory in a systematic way. Many of the results are obtained by utilizing matrix derivatives which in turn are built up from the Kronecker product and vec-operator. The matrix normal, Wishart and elliptical distributions are studied in detail. In particular, several moment relations are given. Together with the derivatives of density functions, formulae are presented for density approximations, generalizing classical Edgeworth expansions. The asymptotic distributions of many commonly used statistics are also derived. In the final part of the book the Growth Curve model and its various extensions are studied. The book will be of particular interest to researchers but could also be appropriate as a text-book for graduate courses on multivariate analysis or matrix algebra. ... Read more

Book Description

In a sign-solvable linear system, the signs of the coefficients determine the signs of some entries in the solution.This type of system is part of a larger study that helps researchers understand if properties of a matrix can be determined from combinatorial arrangements of its elements. In this book, the authors present the diffuse body of literature on sign-solvability as a coherent whole for the first time, giving many new results and proofs and establishing many new connections.Brualdi and Shader describe and comment on algorithms implicit in many of the proofs and their complexity. The book is self-contained, assuming familiarity only with elementary linear algebra and graph theory.Intended primarily for researchers in combinatorics and linear algebra, it should also be of interest to computer scientists, economists, physicists, chemists, and engineers. ... Read more

Reviews (1)

Very abstract
I'm not really a mathematician at heart. I use math and enjoy using it, but never really learned to love it for its own sake. In other words, this book wasn't written for me.

I work with combinatoric problems a fair bit, and hoped that sign-solvable systems (SSS) would be directly applicable to some of my work. I also look at questions where sloppy data prevent exact solutions - if a technique promises at least partial answers when precise answers aren't available, it has my interest. The SSS premise is that, in some cases, I can tell whether parts of my answer are positive, negative, or zero, knowing only whether the inputs were positive, negative, or zero. The simplified character of the questions and answers could possibly work well in special computing environments that I use. I really wanted to like this book and its content.

I just wasn't able to connect these abstractions to my real world, though. The focus of this book is on the abstract structures behind SSS, and on formal proofs about specific features of special cases.

This book does have a practical side. It specifies a number of algorithms for handling sign-solvable systems of various sorts. It would take a lot of effort to reduce these algorithms to practice, but the information is all there. As books of pure advanced math go, this one seems relatively clear and approachable.

Perhaps a more astute reader than me can connect SSS to problems of practical interest. Perhaps, some day, I'll take the time to work through this book in detail. These days, though, I can't spend a lot of time away from the problems I need to solve. Building up a working knowledge of SSS from this book would take intense effort. I really have to put my effort elsewhere. ... Read more

Book Description

This monograph is an accessible account of the normed algebras over the real field, particularly the quaternions and the Cayley numbers. The application of quaternions to spherical geometry and to mechanics is considered and the relation between quaternions and rotations in 3- and 4-dimensional Euclidean space is fully developed. The algebra of complexified quaternions is described and applied to electromagnetism and to special relativity. By looking at a 3-dimensional complex space we explore the use of a quaternion formalism to the Lorentz transformation and we examine the classification of electromagnetic and Weyl tensors. In the final chapter, extensions of quaternion algebra to the alternative non-associative algebra of Cayley numbers are investigated. The standard Cayley number identities are derived and their use in the analysis of 7- and 8-dimensional rotations is studied. Appendices on Clifford algebras and on the use of dynamic computation in Cayley algebra are included.Audience: This volume has been written at a level suitable for final year and postgraduate students. ... Read more

Reviews (1)

Excellent introduction to higher dimensional number systems
As a working mathematician in the field of hypercomplex analysis I've found this book very useful to understand the algebraic and geometric properties of the arithmetic of hypercomplex numbers. Eventhough the book doesn't tell anything about quaternionic analysis, it is helpful as a reference when one has to deal with the algebraic features of these systems.

I think most of the contents of the book are understandable by second or thir year undergrads, after reading Feferman's "The Number Systems", for example. ... Read more

Book Description

The theory of generalized inverses of real or complex matrices is a well-developed and well-documented subject.However, the wider subject of generalized inverses of matrices over rings has reached a state for a comprehensive treatment only recently.The author, who contributed to this development, provides a book for students of the subject.Mathematicians working in g-inverses of matrices, algebraists and control theorists will be interested in the results presented here.The book would also be suitable for graduate courses on G-inverses in algebra. ... Read more

Book Description

With many 'flexible' structures such as large span bridges, tall buildings, towers, cable roofs, etc., being built, the need to understand the dynamics behavior of structures has become a necessity for many engineers. The recent problems with the millinium bridge is simply another reminder. The many devastating earthquakes in many parts of the world leading to severe loss of life in densely inhabited urban areas alos has underlined the need for a fundamental understanding of structural behavior. In addition, by its very nature, dynamic analysis is numerically very intensive and use of computers is obligatory. Although books do exist that cover one or more aspects of dynamic behavior, no book covers in any depth all aspects. This is a unique book which combines the four aspect of Dynamic analysis of structures. The topics covered are: 1. Theory of Dynamic Analysis, 2. Finite Element Analysis, 3. Matrix Routines, 4. Fortran-90 Programs. This book will be an invaluable reference for engineers and graduate students. ... Read more

Book Description

Hardbound. The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume 3 covers Mathematical Approaches to Welfare Economics, including social choice theory, optimal taxation, and optimal growth, together with Mathematical Approaches to Economic Organization and Planning, including organization design and decentralization.

For more information on the Handbooks in Economics series, ... Read more

Book Description

Intended for a serious first course or a second course, this textbook will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, to normal matrices, to spectral decompositions, and to the Jordan form. The authors approach their subject in a comprehensive and accessible manner, presenting notation and terminology clearly and concisely, and providing smooth transitions between topics. The examples and exercises are well designed and will aid diligent students in understanding both computational and theoretical aspects. In all, the straightest, smoothest path to the heart of linear algebra.

* Special Features:
* Provides complete coverage of central material.
* Presents clear and direct explanations.
* Includes classroom tested material.
* Bridges the gap from lower division to upper division work.
* Allows instructors alternatives for introductory or second-level courses. ... Read more

Book Description

Introduction to Large Truncated Toeplitz Matrices is a text on the application of functional analysis and operator theory to some concrete asymptotic problems of linear algebra. The book contains results on the stability of projection methods, deals with asymptotic inverses and Moore-Penrose inversion of large Toeplitz matrices, and embarks on the asymptotic behavoir of the norms of inverses, the pseudospectra, the singular values, and the eigenvalues of large Toeplitz matrices. The approach is heavily based on Banach algebra techniques and nicely demonstrates the usefulness of C*-algebras and local principles in numerical analysis. The book includes classical topics as well as results obtained and methods developed only in the last few years. Though employing modern tools, the exposition is elementary and aims at pointing out the mathematical background behind some interesting phenomena one encounters when working with large Toeplitz matrices. The text is accessible to readers with basic knowledge in functional analysis. It is addressed to graduate students, teachers, and researchers with some inclination to concrete operator theory and should be of interest to everyone who has to deal with infinite matrices (Toeplitz or not) and their large truncations. ... Read more

Book Description

Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms.

Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research. ... Read more