Book Description

This textbook is a new introduction to linear algebra for students who have completed the first year of calculus. In the spirit of modern instruction, this elementary presentation of the important ideas in linear algebra emphasizes conceptual understanding, developing applied examples, and working with realistic numerical data before introducing formal mathematical definition and operations. This text emphasizes geometric, symbolic, and numeric presentations of the subject. The first two chapters cover linear phenomena in both numeric and geometric settings. The symbolic manipulation of vectors and matrices is then introduced as a tool for the study of specific problems. Many examples, student exercises, and group project ideas are included. ... Read more

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Eavesdropping On A Master
A droll explication of techniques that can be applied to understand some of the most important engineering problems: those dealing with vibrations, buckling, and earthquake resistance. While containing substantial theory, this is an applied mathematics text that reads as if you are eavesdropping on the author talking out loud to himself. What sets it off from the crowd of math books are the inside references to Parlett's friends in the business, and the dry wit. It contains NO CODE, yet discusses algorithms in detail, describing where they are good, and where they flop. The reader must pay attention, however, and work through some of the exercises with a calculator (a spreadsheet is handier, in my view). If you are looking for eigenvalues, this text is a necessary part of your toolkit. ... Read more

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Vector Spaces and Matrices in Physics
I am a first year graduate student in physics. I found this book extremely useful. It is very easy to read, easy to understand, and very concise. The material is presented in a logical way and the entire book can be read in a few hours if you are short on time. It is one of my favorite linear algebra books. ... Read more

Book Description

This volume, dedicated to Bernd Silbermann on his sixtieth birthday, collects research articles on Toeplitz matrices and singular integral equations written by leading area experts.

The subjects of the contributions include Banach algebraic methods, Toeplitz determinants and random matrix theory, Fredholm theory and numerical analysis for singular integral equations, and efficient algorithms for linear systems with structured matrices, and reflect Bernd Silbermann's broad spectrum of research interests. The volume also contains a biographical essay and a list of publications.

The book is addressed to a wide audience in the mathematical and engineering sciences. The articles are carefully written and are accessible to motivated readers with basic knowledge in functional analysis and operator theory. ... Read more

Book Description

This is the first book on higher dimensional Hadamard matrices and their applications in telecommunications and information security. It is divided into three parts according to the dimensions of the Hadamard matrices treated. The first part stresses the classical 2-dimensional Walsh and Hadamard matrices. Fast algorithms, updated constructions, existence results, and their generalised forms are presented. The second part deals with the lower-dimensional cases, e.g. 3-, 4-, and 6-dimensional Walsh and Hadamard matrices and transforms. One of the aims of this part is to simplify moving smoothly from 2-dimensional cases to the general higher-dimensional cases. This part concentrates on the 3-dimensional Hadamard and Walsh matrices. Constructions based upon direct multiplication, and upon recursive methods, and perfect binary arrays are also introduced. Another important topic is the existence and construction of 3-dimensional Hadamard matrices of orders 4k and 4k + 2 respectively, and a group of transforms based on 2-, 3-, 4-, and 6-dimensional Walsh--Hadamard matrices and their corresponding fast algorithms.The third part is the key part, which investigates the N-dimensional Hadamard matrices of order 2, which have been proved equivalent to the well-known H-Boolean functions and the perfect binary arrays of order 2. This equivalence motivates a group of perfect results about the enumeration of higher-dimensional Hadamard matrices of order 2. Applications of these matrices to feed forward networking, stream cipher, Bent functions, and error correction codes are presented in turn. After introducing the definitions of the regular, proper, improper, and generalised higher-dimensional Hadamard matrices, many theorems about the existence and constructions are presented. Perfect binary arrays, generalised perfect arrays, and the orthogonal designs are also used to construct new higher-dimensional Hadamard matrices. The many open problems in the study of the theory of higher-dimensional Hadamard matrices, which are also listed in the book, will encourage further research.Audience: This volume will appeal to researchers and graduate students whose work involves signal processing, coding, information security, and applied discrete mathematics. ... Read more

Book Description

Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application.

Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory.

A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.

Book Description

Book Description

The fifth edition of this comprehensive textbook combines and develops concurrently, both classical and matrix-based methods of structural analysis. A new introductory chapter on structural modeling has been added. The suitability of modeling structures as beams, plane or space frames and trusses, plane grids or assemblages of finite elements is discussed in this chapter, along with idealization of load, anticipated deformations, sketching deflected shapes, and bending moment diagrams. With new solved examples and problems added, the book now has over 100 worked examples and more than 350 problems with answers. ... Read more

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Jack of all trades but master of none!
Within 800 pages, the authors have tried to include everything from basic structural equilibrium to finite element method. The effect is obvious, it has touched all topics superficially without any details. It has finished structural dynamics in one chapter and finite elements in two chapters! Examples lack details and jumps steps and are too complex to comprehend. Moreover it contains numerous printing mistakes. Theories are too obscure to follow. In overall, not a good book. ... Read more

Book Description

This text/reference is the most up-to-date volume on nonnegative matrices in print and presents much material that was previously available only in research papers. It is the only book to cover the van der Waerden conjecture on permanents. There is also coverage of doubly stochastic matrices and inverse problems. The material has abundant connections to graph theory, incidence geometry, stochastic processes, functional analysis, and quadratic forms. Each chapter contains a comprehensive set of problems and a substantial list of references. ... Read more

Book Description