Numerical Linear Algebra with Applications

1st Edition


Print ISBN: 9780123944351
eBook ISBN: 9780123947840
Imprint: Academic Press
Published Date: 2nd September 2014
Page Count: 628
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119.95 + applicable tax
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Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications 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. It provides necessary mathematical background information for those who want to learn to solve linear algebra problems, and offers a thorough explanation of the issues and methods for practical computing, using MATLAB as the vehicle for computation. The 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.

Key Features

  • 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


Graduate or advanced undergraduate students in engineering, science, and mathematics, 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.

Table of Contents

  • Dedication
  • List of Figures
  • List of Algorithms
  • Preface

    • Topics
    • Intended Audience
    • Ways to Use the Book
    • Matlab Library
    • Supplement
    • Acknowledgments
  • Chapter 1: Matrices

    • Abstract
    • 1.1 Matrix Arithmetic
    • 1.2 Linear Transformations
    • 1.3 Powers of Matrices
    • 1.4 Nonsingular Matrices
    • 1.5 The Matrix Transpose and Symmetric Matrices
    • 1.6 Chapter Summary
    • 1.7 Problems
  • Chapter 2: Linear Equations

    • Abstract
    • 2.1 Introduction to Linear Equations
    • 2.2 Solving Square Linear Systems
    • 2.3 Gaussian Elimination
    • 2.4 Systematic Solution of Linear Systems
    • 2.5 Computing the Inverse
    • 2.6 Homogeneous Systems
    • 2.7 Application: A Truss
    • 2.8 Application: Electrical Circuit
    • 2.9 Chapter Summary
    • 2.10 Problems
  • Chapter 3: Subspaces

    • Abstract
    • 3.1 Introduction
    • 3.2 Subspaces of n
    • 3.3 Linear Independence
    • 3.4 Basis of a Subspace
    • 3.5 The Rank of a Matrix
    • 3.6 Chapter summary
    • 3.7 Problems
  • Chapter 4: Determinants

    • Abstract
    • 4.1 Developing the Determinant of A 2 × 2 and A 3 × 3 matrix
    • 4.2 Expansion by Minors
    • 4.3 Computing a Determinant Using Row Operations
    • 4.4 Application: Encryption
    • 4.5 Chapter Summary
    • 4.6 Problems
  • Chapter 5: Eigenvalues and Eigenvectors

    • Abstract
    • 5.1 Definitions and Examples
    • 5.2 Selected Properties of Eigenvalues and Eigenvectors
    • 5.3 Diagonalization
    • 5.4 Applications
    • 5.5 Computing Eigenvalues and Eigenvectors Using Matlab
    • 5.6 Chapter Summary
    • 5.7 Problems<


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© Academic Press 2014
Academic Press
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"An important part of the book deals with iterative methods for solving large sparse systems. We can find here Jacobi, Gauss-Seidel and successive overrelaxation (SOR) methods, as well as Krylov subspace methods..." --Zentralblatt Math

"...this is a book that merits careful consideration as a possible text for a course in numerical linear algebra, particularly one stressing applications to engineering and other areas of science." --MAA Reviews, January 2015