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Linear Algebra and Its Applications

Linear Algebra and Its Applications - 2nd edition

ISBN13: 978-0201824780

Cover of Linear Algebra and Its Applications 2ND 97 (ISBN 978-0201824780)
ISBN13: 978-0201824780
ISBN10: 0201824787
Cover type:
Edition/Copyright: 2ND 97
Publisher: Addison-Wesley Longman, Inc.
Published: 1997
International: No

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Linear Algebra and Its Applications - 2ND 97 edition

ISBN13: 978-0201824780

David C. Lay

ISBN13: 978-0201824780
ISBN10: 0201824787
Cover type:
Edition/Copyright: 2ND 97
Publisher: Addison-Wesley Longman, Inc.

Published: 1997
International: No

Linear algebra is relatively easy for students when the material is presented in a familiar, concrete setting, but it becomes much more difficult when abstract concepts are introduced. Certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood but are fundamental to the study of linear algebra. The author introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts more accessible and student understanding is reinforced through True-or-False questions, practice problems, and the use of technologies, such as MATLAB, for solving large matrix exercises.


  • Technology exercises, using real-data sets and citing sources, provide realistic exercises designed to be completed with technology.
  • True-or-False questions in the exercise sets encourage critical thinking and discussion.
  • To enhance clarity, 25 percent of the art has been revised.
  • This edition includes new and revised Numerical Notes, some of which address MAPLE.
  • Chapters 1 and 2 of the first edition were combined and streamlined to allow for a smoother entry into the course.
  • Early coverage of Subspaces of Rn in new Section 2.9 lets users skip the bulk of material in Chapters 3 and 4 and go straight to the Eigenvalue section in Chapter 5. Those teaching a standard-paced course would cover Chapters 2, 3, and 4, skipping 2.9.
  • LU Factorization coverage is emphasized.
  • Difference equations, particularly important to a junior-level course, have been added to Chapter 6.
  • This text includes such up-to-date topics as difference equations (dynamical systems); LU and QR factorizations; and spectoral decomposition.
  • The Application section at the end of each chapter provide a broad selection of applications from engineering, physics, computer science, mathematics, economics, and statistics.
  • Practice Problems & Answers, unique to this text, focus on points that may cause students difficulty. They are placed before the section exercise sets as a warmup; answers follow the exercise sets.
  • The Supplemental Exercises following each chapter include theoretical and proof-oriented multiconcept stretch exercises and writing exercises that require written justification of a true-or-false answer.
  • A glossary of key terms is included.
  • Numerical Notes, designed to make the reader more computer-aware, are given throughout the text, indicating technology-related issues that deserve further study.

Author Bio

Lay, David C. : University of Maryland Baltimore

Table of Contents

Chapter 1: Linear Equations in Linear Algebra

Systems of Linear Equations
Row Reduction and Echelon Forms
Vector Equations
The Matrix Equation Ax = b
Solution Sets of Linear Systems
Linear Independence
Introduction to Linear Transformations
The Matrix of a Linear Transformation
Linear Models in Business, Science, and Engineering

Chapter 2: Matrix Algebra

Matrix Operations
The Inverse of a Matrix
Characterizations of Invertible Matrices
Partitioned Matrices
Matrix Factorizations
Iterative Solutions of Linear Systems
The Leontief Input­Output Model
Applications to Computer Graphics
Subspaces of Rn

Chapter 3: Determinants

Introduction to Determinants
Properties of Determinants
Cramer's Rule, Volume, and Linear Transformations

Chapter 4: Vector Spaces

Vector Spaces and Subspaces
Null Spaces, Column Spaces, and Linear Transformations
Linearly Independent Sets; Bases
Coordinate Systems
The Dimension of a Vector Space
Change of Basis
Applications to Difference Equations
Applications to Markov Chains

Chapter 5: Eigenvalues and Eigenvectors

Eigenvectors and Eigenvalues
The Characteristic Equation
Eigenvectors and Linear Transformations
Complex Eigenvalues
Discrete Dynamical Systems
Applications to Differential Equations
Iterative Estimates for Eigenvalues

Chapter 6: Orthogonality and Least-Squares

Inner Product, Length, and Orthogonality
Orthogonal Sets
Orthogonal Projections
The Gram­Schmidt Process
Least-Squares Problems
Applications to Linear Models
Inner Product Spaces
Applications of Inner Product Spaces

Chapter 7: Symmetric Matrices and Quadratic Forms

Diagonalization of Symmetric Matrices
Quadratic Forms
Constrained Optimization
The Singular Value Decomposition
Applications to Image Processing and Statistics

Uniqueness of the Reduced Echelon Form
Complex Numbers

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