Vectors and Matrices

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Author: Pamela Liebeck

Publisher: Elsevier

ISBN: 1483280438

Category: Mathematics

Page: 192

View: 6595

Vectors and Matrices provides a progressive approach to vectors and matrices. The first half of this book is devoted to geometry, introducing matrices through its association with geometry mappings, while the rest of the chapters focus on the importance of matrices in non-geometric situations, such as the theory of linear equations and eigenvector theory. The power of eigenvector theory and its application to some problems in biology, probability, and genetics are also reviewed. Other topics include the product of scalar and vector, vector equation of a line, linear dependence, three-dimensional mappings, and orthogonal matrices. The transpose of a matrix and vector, rectangular matrices, inverse of a square matrix, and eigenvectors of a matrix are likewise emphasized in this text. This publication is beneficial to students and researchers conducting work on vectors and matrices.

Introduction to Matrices and Vectors

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Author: Jacob T. Schwartz

Publisher: Courier Corporation

ISBN: 0486143708

Category: Mathematics

Page: 192

View: 9453

DIVIn this concise undergraduate text, the first three chapters present the basics of matrices — in later chapters the author shows how to use vectors and matrices to solve systems of linear equations. 1961 edition. /div

Vectors, Matrices and C++ Code

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Author: Sergio Pissanetzky

Publisher: N.A

ISBN: 0976277506

Category: Computers

Page: 365

View: 1637

Presented here is an integrated approach - perhaps the first in its class - of the basics of vector and matrix Algebra at College level, with the object-oriented C++ code that implements the vector and matrix objects and brings them to life. Thinking in terms of objects is the natural way of thinking. The concept of object has existed in Science for centuries. More recently, objects were introduced in Computation, and object-oriented programming languages were created. Yet the concept of object is not routinely used when teaching Science, and the idea that objects can come alive in a computer has not yet been fully exploited.This book integrates basic vector and matrix Algebra with object-oriented concepts and the actual code implementing them. It is both a textbook and a software release, complete withsoftware documentation and the mathematical background that supports the code. The source code is included by download and readers can use it for their own programming. The reader will need a basic knowledge of Mathematical notation, Algebra and Trigonometry, but familiarity with C++ is not required because a course on C++ is also included. You should read this book if you are a developer who needs a background in vector or matrix algebra, a science student who needs tolearn C++, a scientist who needs to write advanced code but can't waste time developing the basics, or you just need ready-to-use C++ source code for your project.

Vectors in Three-Dimensional Space

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Author: J. S. R. Chisholm

Publisher: CUP Archive

ISBN: 9780521292894

Category: Mathematics

Page: 293

View: 9821

This book deals with vector algebra and analysis and with their application to three-dimensional geometry and the analysis of fields in three dimensions. While many treatments of the application of vectors have approached the fundamentals of the subject intuitively, assuming some prior knowledge of Euclidean and Cartesian geometry, Professor Chrisholm here bases the subject on the axioms of linear space algebra, which are fundamental to many branches of mathematics. While developing the properties of vectors from axioms, however, he continually emphasizes the geometrical interpretation of vector algebra in order to build up intuitive relations between the algebraic equations and geometrical concepts. Throughout, examples are used to illustrate the theory being developed; several sets of problems are incorporate in each chapter, and outline answers to many of these are given. Written primarily for undergraduate mathematicians in the early part of their courses, this lucidly written book will also appeal to mathematical physicists and to mathematically inclined engineers.

Vectors, Matrices and Geometry

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Author: K.T. Leung,S.N. Suen

Publisher: Hong Kong University Press

ISBN: 9622093604

Category: Mathematics

Page: 356

View: 7582

This book is the last volume of a three-book series written for Sixth Form students and first-year undergraduates. It introduces the important concepts of finite-dimensional vector spaces through the careful study of Euclidean geometry. In turn, methods of linear algebra are then used in the study of coordinate transformations through which a complete classification of conic sections and quadric surfaces is obtained. The book concludes with a detailed treatment of linear equations in n variables in the language of vectors and matrices. Illustrative examples are included in the main text and numerous exercises are given in each section. The other books in the series are Fundamental Concepts of Mathematics (published 1988) and Polynomials and Equations (published 1992).

Probability, Markov Chains, Queues, and Simulation

The Mathematical Basis of Performance Modeling

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Author: William J. Stewart

Publisher: Princeton University Press

ISBN: 1400832810

Category: Mathematics

Page: 776

View: 4022

Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises

Matrix Algebra

Theory, Computations, and Applications in Statistics

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Author: James E. Gentle

Publisher: Springer Science & Business Media

ISBN: 0387708731

Category: Mathematics

Page: 530

View: 4342

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed 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.

Matrix Vector Analysis

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Author: Richard L. Eisenman

Publisher: Courier Corporation

ISBN: 0486154572

Category: Mathematics

Page: 320

View: 3789

This outstanding text and reference for upper-level undergraduates features extensive problems and solutions in its application of matrix ideas to vector methods for a synthesis of pure and applied mathematics. 1963 edition. Includes 121 figures.

Applied Longitudinal Analysis

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Author: Garrett M. Fitzmaurice,Nan M. Laird,James H. Ware

Publisher: John Wiley & Sons

ISBN: 1118551796

Category: Mathematics

Page: 740

View: 9130

Praise for the First Edition ". . . [this book] should be on the shelf of everyone interestedin . . . longitudinal data analysis." —Journal of the American Statistical Association Features newly developed topics and applications of theanalysis of longitudinal data Applied Longitudinal Analysis, Second Edition presentsmodern methods for analyzing data from longitudinal studies and nowfeatures the latest state-of-the-art techniques. The bookemphasizes practical, rather than theoretical, aspects of methodsfor the analysis of diverse types of longitudinal data that can beapplied across various fields of study, from the health and medicalsciences to the social and behavioral sciences. The authors incorporate their extensive academic and researchexperience along with various updates that have been made inresponse to reader feedback. The Second Edition features six newlyadded chapters that explore topics currently evolving in the field,including: Fixed effects and mixed effects models Marginal models and generalized estimating equations Approximate methods for generalized linear mixed effectsmodels Multiple imputation and inverse probability weightedmethods Smoothing methods for longitudinal data Sample size and power Each chapter presents methods in the setting of applications todata sets drawn from the health sciences. New problem sets havebeen added to many chapters, and a related website features sampleprograms and computer output using SAS, Stata, and R, as well asdata sets and supplemental slides to facilitate a completeunderstanding of the material. With its strong emphasis on multidisciplinary applications andthe interpretation of results, Applied LongitudinalAnalysis, Second Edition is an excellent book for courses onstatistics in the health and medical sciences at theupper-undergraduate and graduate levels. The book also serves as avaluable reference for researchers and professionals in themedical, public health, and pharmaceutical fields as well as thosein social and behavioral sciences who would like to learn moreabout analyzing longitudinal data.

Vectors and Matrices

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Author: Harold Andrew Elliott

Publisher: N.A

ISBN: N.A

Category: Vector algebra

Page: 296

View: 9681

Matrix Methods of Structural Analysis

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Author: R. K. Livesley

Publisher: Elsevier

ISBN: 1483136264

Category: Technology & Engineering

Page: 280

View: 1423

Matrix Methods of Structural Analysis presents how concepts and notations of matrix algebra can be applied to arriving at general systematic approach to structure analysis. The book describes the use of matrix notation in structural analysis as being theoretically both compact and precise, but also, quite general. The text also presents, from the practical point of view, matrix notation as providing a systematic approach to the analysis of structures related to computer programming. Matrix algebraic methods are useful in repeated calculations where manual work becomes tedious. The Gaus-Seidel method and linear programming are two methods to use in solving simultaneous equations. The book then describes the notation for loads and displacements, on sign conventions, stiffness and flexibility matrices, and equilibrium and compatibility conditions. The text discusses the formulation of the equilibrium method using connection matrices and an alternative method. The book evaluates the compatibility method as programmed in a computer; and it discusses the analysis of a pin-jointed truss and of a rigid-jointed truss. The book presents some problems when using computers for analyzing structures, such as decision strategy, accuracy, and checks conducted on handling large matrices. The text also analyzes structures that behave in a non-linear manner. The book is suitable for structural engineers, physicist, civil engineers, and students of architectural design.

TORRIX

a programming system for operations on vectors and matrices over arbitrary fields and of variable size

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Author: S. G. van der Meulen,M. Veldhorst

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 231

View: 5340

Mathematical Objects in C++

Computational Tools in A Unified Object-Oriented Approach

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Author: Yair Shapira

Publisher: CRC Press

ISBN: 9781439811481

Category: Computers

Page: 609

View: 3540

Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. Object-oriented implementation of three-dimensional meshes facilitates understanding of their mathematical nature. Requiring no prerequisites, the text covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. Exercises and solutions make the book suitable for classroom use and a supporting website supplies downloadable code.

MATLAB For Dummies

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Author: Jim Sizemore,John Paul Mueller

Publisher: John Wiley & Sons

ISBN: 1118820037

Category: Technology & Engineering

Page: 432

View: 4293

Plot graphs, solve equations, and write code in a flash! If you work in a STEM field, chances are you'll be using MATLABon a daily basis. MATLAB is a popular and powerful computationaltool and this book provides everything you need to startmanipulating and plotting your data. MATLAB has rapidly become thepremier data tool, and MATLAB For Dummies is a comprehensiveguide to the fundamentals. MATLAB For Dummies guides youthrough this complex computational language from installation tovisualization to automation. Learn MATLAB's language fundamentals including syntax,operators, and data types Understand how to use the most important window in MATLAB– the Command Window Get the basics of linear algebra to get up and running withvectors, matrices, and hyperspace Automate your work with programming scripts and functions Plot graphs in 2D and 3D to visualize your data Includes a handy guide for MATLAB's functions and plottingroutines MATLAB is an essential part of the analysis arsenal andMATLAB For Dummies provides clear, thorough guidance to getthe most out of your data.

Matrices and Tensors in Physics

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Author: A. W. Joshi

Publisher: New Age International

ISBN: 9788122405637

Category: Calculus of tensors

Page: 342

View: 2363

This updated edition contains a good deal of new and relevant material including Bessel inequality, vector spaces of functions, physical laws and invariance principle, invariance in 3-D Newtonian and 4-D Minkowski spaces, fully antisymmetric tensors and their contraction. Discusses normal matrices and features a proof of the general theorem that a matrix posesses a complete set of orthonormal eigenvectors if and only if it is a normal matrix. Over 200 exercises and 100+ solved problems help students grasp the concepts presented.