This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.

This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.

As discrete models and computing have become more common, there is a need to study matrix computation and numerical linear algebra. Encompassing a diverse mathematical core, Elements of Matrix Modeling and Computing with MATLAB examines a variety of applications and their modeling processes, showing you how to develop matrix models and solve algebraic systems. Emphasizing practical skills, it creates a bridge from problems with two and three variables to more realistic problems that have additional variables. Elements of Matrix Modeling and Computing with MATLAB focuses on seven basic applications: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. These applications are developed from very simple to more complex models. To explain the processes, the book explores numerous topics in linear algebra, including complex numbers and functions, matrices, algebraic systems, curve fitting, elements of linear differential equations, transform methods, and tools of computation. For example, the author uses linearly independent vectors and subspaces to explain over- and under-determined systems, eigenvalues and eigenvectors to solve initial value problems, and discrete Fourier transforms to perform image filtering in the frequency domain. Although the primary focus is to cultivate calculation skills by hand, most chapters also include MATLAB to help with more complicated calculations.

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work in linear algebra with ease. In addition to exploring MATLAB’s matrix algebra capabilities, it describes the MATLAB commands that are used to create two- and three-dimensional graphics, including explicit, implicit and parametric curve and surface plotting, and various methods of data representation. Methods for solving systems of equations are detailed.

Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

The development of the internationally standardized language ALGOL has made it possible to prepare procedures which can be used without modification whenever a computer with an ALGOL translator is available. Volume Ia in this series gave details of the restricted version of ALGOL which is to be employed throughout the Handbook, and volume Ib described its implementation on a computer. Each of the subsequent volumes will be devoted to a presentation of the basic algorithms in some specific areas of numerical analysis. This is the first such volume and it was feIt that the topic Linear Algebra was a natural choice, since the relevant algorithms are perhaps the most widely used in numerical analysis and have the advantage of forming a weil defined dass. The algorithms described here fall into two main categories, associated with the solution of linear systems and the algebraic eigenvalue problem respectively and each set is preceded by an introductory chapter giving a comparative assessment.

A revised textbook for introductory courses in numerical methods, MATLAB and technical computing, which emphasises the use of mathematical software.

A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."

Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra - Detailed explanations and examples - A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Examples from engineering and science applications