Vectors and Matrices

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Author: Pamela Liebeck

Publisher: Elsevier

ISBN: 1483280438

Category: Mathematics

Page: 192

View: 3900

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: 8464

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

Vector Spaces and Matrices in Physics

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Author: M. C. Jain

Publisher: CRC Press

ISBN: 9780849309786

Category: Mathematics

Page: 183

View: 6971

The theory of vector spaces and matrices is an essential part of the mathematical background required by physicists. Most books on the subject, however, do not adequately meet the requirements of physics courses-they tend to be either highly mathematical or too elementary. Books that focus on mathematical theory may render the subject too dry to hold the interest of physics students, while books that are more elementary tend to neglect some topics that are vital in the development of physical theories. In particular, there is often very little discussion of vector spaces, and many books introduce matrices merely as a computational tool. Vector Spaces and Matrices in Physics fills the gap between the elementary and the heavily mathematical treatments of the subject with an approach and presentation ideal for graduate-level physics students. After building a foundation in vector spaces and matrix algebra, the author takes care to emphasize the role of matrices as representations of linear transformations on vector spaces, a concept of matrix theory that is essential for a proper understanding of quantum mechanics. He includes numerous solved and unsolved problems, and enough hints for the unsolved problems to make the book self-sufficient. Developed through many years of lecture notes, Vector Spaces and Matrices in Physics was written primarily as a graduate and post-graduate textbook and as a reference for physicists. Its clear presentation and concise but thorough coverage, however, make it useful for engineers, chemists, economists, and anyone who needs a background in matrices for application in other areas.

Vectors, Matrices and C++ Code

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Author: Sergio Pissanetzky

Publisher: N.A

ISBN: 0976277506

Category: Computers

Page: 365

View: 5961

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 and Matrices

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Author: Harold Andrew Elliott

Publisher: N.A

ISBN: N.A

Category: Vector algebra

Page: 296

View: 3348

Matrix Vector Analysis

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Author: Richard L. Eisenman

Publisher: Courier Corporation

ISBN: 0486154572

Category: Mathematics

Page: 320

View: 3428

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.

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: 986

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.

Vector Spaces and Matrices

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Author: Robert M. Thrall,Leonard Tornheim

Publisher: Courier Corporation

ISBN: 0486321053

Category: Mathematics

Page: 336

View: 5758

Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.

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: 348

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

ISBN: 3319648675

Category: Mathematics

Page: 648

View: 6197

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.

Vectors in Three-Dimensional Space

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Author: J. S. R. Chisholm

Publisher: CUP Archive

ISBN: 9780521292894

Category: Mathematics

Page: 293

View: 2786

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.

Circuits, Matrices and Linear Vector Spaces

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Author: Lawrence P. Huelsman

Publisher: Courier Corporation

ISBN: 0486280446

Category: Technology & Engineering

Page: 304

View: 1958

This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.

Introduction to Vectors and Tensors

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Author: Ray M. Bowen,Chao-cheng Wang

Publisher: Courier Corporation

ISBN: 048646914X

Category: Mathematics

Page: 520

View: 6327

This convenient single-volume compilation of two texts offers both an introduction and an in-depth survey. Geared toward engineering and science students rather than mathematicians, its less rigorous treatment focuses on physics and engineering applications. A practical reference for professionals, it is suitable for advanced undergraduate and graduate students. 1976 edition.

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: 9789061961529

Category: Mathematics

Page: 231

View: 3403

Majorization and Matrix-monotone Functions in Wireless Communications

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Author: Eduard Jorswieck,Holger Boche

Publisher: Now Publishers Inc

ISBN: 160198040X

Category: Technology & Engineering

Page: 153

View: 6602

Majorization Theory and Matrix-Monotone Functions in Wireless Communications, reviews the basic definitions of Majorization Theory and Matrix-Monotone Functions, describing their concepts clearly with many illustrative examples. In addition to this tutorial, new results are presented with respect to Schur-convex functions and regarding the properties of matrix-monotone functions. The approach taken by the authors provides a valuable overview of the basic techniques for readers who are new to the subject. They then proceed to show in separate chapters the cutting edge applications of the two basic theories in wireless communications. Majorization Theory and Matrix-Monotone Functions in Wireless Communications is an invaluable resource for students, researchers and practitioners involved in the state-of-the-art design of wireless communication systems.

Linear Algebra For Dummies

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Author: Mary Jane Sterling

Publisher: John Wiley & Sons

ISBN: 0470538163

Category: Mathematics

Page: 384

View: 8304

Learn to: Solve linear algebra equations in several ways Put data in order with matrices Determine values with determinants Work with eigenvalues and eigenvectors Your hands-on guide to real-world applications of linear algebra Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction. Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices Open the book and find: Theoretical and practical ways of solving linear algebra problems Definitions of terms throughout and in the glossary New ways of looking at operations How linear algebra ties together vectors, matrices, determinants, and linear transformations Ten common mathematical representations of Greek letters Real-world applications of matrices and determinants

Complex Numbers and Vectors

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Author: Les Evans

Publisher: Aust Council for Ed Research

ISBN: 0864315325

Category: Education

Page: 168

View: 6471

Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries of complex numbers. The text includes historical and background material, discussion of key concepts, skills and processes, commentary on teaching and learning approaches, comprehensive illustrative examples with related tables, graphs and diagrams throughout, references for each chapter (text and web-based), student activities and sample solution notes, and an extensive bibliography.

Generalized Vectorization, Cross-Products, and Matrix Calculus

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Author: Darrell A. Turkington

Publisher: Cambridge University Press

ISBN: 1139620487

Category: Business & Economics

Page: N.A

View: 3011

This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators and a Lagrangian multiplier test for endogeneity.

Applied Linear Algebra and Matrix Analysis

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Author: Thomas S. Shores

Publisher: Springer Science & Business Media

ISBN: 0387489479

Category: Mathematics

Page: 384

View: 6874

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.