Matrices And Linear Programming With Applications

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Coding the Matrix

Author : Philip N. Klein
Publisher :
ISBN 13 : 9780615856735
Total Pages : 530 pages
Book Rating : 4.8/5 (567 download)

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Book Synopsis Coding the Matrix by : Philip N. Klein

Download or read book Coding the Matrix written by Philip N. Klein and published by . This book was released on 2013-07 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program" A new edition of this text, incorporating corrections and an expanded index, has been issued as of September 4, 2013, and will soon be available on Amazon.

Linear and Nonlinear Programming with Maple

Author : Paul E. Fishback
Publisher : CRC Press
ISBN 13 : 1420090658
Total Pages : 410 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Linear and Nonlinear Programming with Maple by : Paul E. Fishback

Download or read book Linear and Nonlinear Programming with Maple written by Paul E. Fishback and published by CRC Press. This book was released on 2009-12-09 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications Supplies enough mathematical rigor yet accessible enough for undergraduates Integrating a hands-on learning approach, a strong linear algebra focus, MapleTM software, and real-world applications, Linear and Nonlinear Programming with MapleTM: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Essential linear algebra tools Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms. Maple enhances conceptual understanding and helps tackle problems Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized real-world applications. Hands-on activities that engage students Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.

Orthogonal Sets and Polar Methods in Linear Algebra

Author : Enrique Castillo
Publisher : John Wiley & Sons
ISBN 13 : 1118031148
Total Pages : 422 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Orthogonal Sets and Polar Methods in Linear Algebra by : Enrique Castillo

Download or read book Orthogonal Sets and Polar Methods in Linear Algebra written by Enrique Castillo and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique, applied approach to problem solving in linearalgebra Departing from the standard methods of analysis, this unique bookpresents methodologies and algorithms based on the concept oforthogonality and demonstrates their application to both standardand novel problems in linear algebra. Covering basic theory oflinear systems, linear inequalities, and linear programming, itfocuses on elegant, computationally simple solutions to real-worldphysical, economic, and engineering problems. The authors clearlyexplain the reasons behind the analysis of different structures andconcepts and use numerous illustrative examples to correlate themathematical models to the reality they represent. Readers aregiven precise guidelines for: * Checking the equivalence of two systems * Solving a system in certain selected variables * Modifying systems of equations * Solving linear systems of inequalities * Using the new exterior point method * Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables,end-of-chapter exercises as well as Java and Mathematica programsavailable from the authors' Web site, this is an invaluabletext/reference for mathematicians, engineers, applied scientists,and graduate students in mathematics.

Matrices in Control Theory

Author : Stephen Barnett
Publisher : Van Nostrand Reinhold Company
ISBN 13 :
Total Pages : 244 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Matrices in Control Theory by : Stephen Barnett

Download or read book Matrices in Control Theory written by Stephen Barnett and published by Van Nostrand Reinhold Company. This book was released on 1971 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Linear and Matrix Algebra

Author : Nathaniel Johnston
Publisher : Springer Nature
ISBN 13 : 3030528111
Total Pages : 482 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Introduction to Linear and Matrix Algebra by : Nathaniel Johnston

Download or read book Introduction to Linear and Matrix Algebra written by Nathaniel Johnston and published by Springer Nature. This book was released on 2021-05-19 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software. Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.

Introduction to Applied Linear Algebra

Author : Stephen Boyd
Publisher : Cambridge University Press
ISBN 13 : 1316518965
Total Pages : 477 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Introduction to Applied Linear Algebra by : Stephen Boyd

Download or read book Introduction to Applied Linear Algebra written by Stephen Boyd and published by Cambridge University Press. This book was released on 2018-06-07 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Linear Programming and Its Applications

Author : James K. Strayer
Publisher : Springer Science & Business Media
ISBN 13 : 1461210097
Total Pages : 274 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linear Programming and Its Applications by : James K. Strayer

Download or read book Linear Programming and Its Applications written by James K. Strayer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Programming and Its Applications is intended for a first course in linear programming, preferably in the sophomore or junior year of the typical undergraduate curriculum. The emphasis throughout the book is on linear programming skills via the algorithmic solution of small-scale problems, both in the general sense and in the specific applications where these problems naturally occur. The book arose from lecture notes prepared during the years 1985-1987 while I was a graduate assistant in the Department of Mathematics at The Pennsylvania State University. I used a preliminary draft in a Methods of Management Science class in the spring semester of 1988 at Lock Haven University. Having been extensively tried and tested in the classroom at various stages of its development, the book reflects many modifications either suggested directly by students or deemed appropriate from responses by students in the classroom setting. My primary aim in writing the book was to address common errors and difficulties as clearly and effectively as I could.

Matrix Analysis and Applied Linear Algebra

Author : Carl D. Meyer
Publisher : SIAM
ISBN 13 : 0898714540
Total Pages : 729 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Matrix Analysis and Applied Linear Algebra by : Carl D. Meyer

Download or read book Matrix Analysis and Applied Linear Algebra written by Carl D. Meyer and published by SIAM. This book was released on 2000-06-01 with total page 729 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book avoids the traditional definition-theorem-proof format; instead a fresh approach introduces a variety of problems and examples all in a clear and informal style. The in-depth focus on applications separates this book from others, and helps students to see how linear algebra can be applied to real-life situations. Some of the more contemporary topics of applied linear algebra are included here which are not normally found in undergraduate textbooks. Theoretical developments are always accompanied with detailed examples, and each section ends with a number of exercises from which students can gain further insight. Moreover, the inclusion of historical information provides personal insights into the mathematicians who developed this subject. The textbook contains numerous examples and exercises, historical notes, and comments on numerical performance and the possible pitfalls of algorithms. Solutions to all of the exercises are provided, as well as a CD-ROM containing a searchable copy of the textbook.

Optimization Using Linear Programming

Author : A. J. Metei
Publisher : Mercury Learning and Information
ISBN 13 : 1683923464
Total Pages : 435 pages
Book Rating : 4.6/5 (839 download)

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Book Synopsis Optimization Using Linear Programming by : A. J. Metei

Download or read book Optimization Using Linear Programming written by A. J. Metei and published by Mercury Learning and Information. This book was released on 2019-03-21 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for engineers, mathematicians, computer scientists, financial analysts, and anyone interested in using numerical linear algebra, matrix theory, and game theory concepts to maximize efficiency in solving applied problems. The book emphasizes the solution of various types of linear programming problems by using different types of software, but includes the necessary definitions and theorems to master theoretical aspects of the topics presented. Features: Emphasizes the solution of various types of linear programming problems by using different kinds of software, e.g., MS-Excel, solutions of LPPs by Mathematica, MATLAB, WinQSB, and LINDO Provides definitions, theorems, and procedures for solving problems and all cases related to various linear programming topics Includes numerous application examples and exercises, e.g., transportation, assignment, and maximization Presents numerous topics that can be used to solve problems involving systems of linear equations, matrices, vectors, game theory, simplex method, and more.

Understanding and Using Linear Programming

Author : Jiri Matousek
Publisher : Springer Science & Business Media
ISBN 13 : 3540307176
Total Pages : 230 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Understanding and Using Linear Programming by : Jiri Matousek

Download or read book Understanding and Using Linear Programming written by Jiri Matousek and published by Springer Science & Business Media. This book was released on 2007-07-04 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".

Linear Programming with MATLAB

Author : Michael C. Ferris
Publisher : SIAM
ISBN 13 : 0898716438
Total Pages : 270 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Linear Programming with MATLAB by : Michael C. Ferris

Download or read book Linear Programming with MATLAB written by Michael C. Ferris and published by SIAM. This book was released on 2007-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to linear programming using MATLAB® software to elucidate the development of algorithms and theory. Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required.

Nonnegative Matrices and Applications

Author : R. B. Bapat
Publisher : Cambridge University Press
ISBN 13 : 0521571677
Total Pages : 351 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Nonnegative Matrices and Applications by : R. B. Bapat

Download or read book Nonnegative Matrices and Applications written by R. B. Bapat and published by Cambridge University Press. This book was released on 1997-03-28 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

Theory of Linear and Integer Programming

Author : Alexander Schrijver
Publisher : John Wiley & Sons
ISBN 13 : 9780471982326
Total Pages : 488 pages
Book Rating : 4.9/5 (823 download)

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Book Synopsis Theory of Linear and Integer Programming by : Alexander Schrijver

Download or read book Theory of Linear and Integer Programming written by Alexander Schrijver and published by John Wiley & Sons. This book was released on 1998-06-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index

Mathematical Introduction to Linear Programming and Game Theory

Author : Louis Brickman
Publisher : Springer Science & Business Media
ISBN 13 : 1461245400
Total Pages : 140 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematical Introduction to Linear Programming and Game Theory by : Louis Brickman

Download or read book Mathematical Introduction to Linear Programming and Game Theory written by Louis Brickman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableau the beautiful termination theorem of R.G. Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games. The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity.

An Introduction to Linear Programming and Game Theory

Author : Paul R. Thie
Publisher : John Wiley & Sons
ISBN 13 : 1118165454
Total Pages : 476 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis An Introduction to Linear Programming and Game Theory by : Paul R. Thie

Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the Second Edition: "This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications." —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

Elementary Linear Programming with Applications

Author : Bernard Kolman
Publisher : Elsevier
ISBN 13 : 148326968X
Total Pages : 417 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Elementary Linear Programming with Applications by : Bernard Kolman

Download or read book Elementary Linear Programming with Applications written by Bernard Kolman and published by Elsevier. This book was released on 2014-05-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful.

Linear Programming Using MATLAB®

Author : Nikolaos Ploskas
Publisher : Springer
ISBN 13 : 3319659197
Total Pages : 646 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Linear Programming Using MATLAB® by : Nikolaos Ploskas

Download or read book Linear Programming Using MATLAB® written by Nikolaos Ploskas and published by Springer. This book was released on 2017-10-28 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting rules, basis update methods, and sensitivity analysis.