Rent 9780201658590 | Introduction to Linear Algebra | Johnson, Lee W.; Riess, R. Dean; Arnold, Jimmy T. @knetbooks.com

Summary Table of Contents

Introduction to Linear Algebra, 5/e is a foundation book that bridges both practical computation and theoretical principles. Due to its flexible table of contents, the book is accessible for both students majoring in the scientific, engineering, and social sciences, as well as students that want an introduction to mathematical abstraction and logical reasoning. In order to achieve the text's flexibility, the book centers on 3 principal topics: matrix theory and systems of linear equations, elementary vector space concepts, and the eigenvalue problem. This highly adaptable text can be used for a one-quarter or one-semester course at the sophomore/junior level, or for a more advanced class at the junior/senior level.

Matrices and Systems of Linear Equations

(112)

Introduction to Matrices and Systems of Linear Equations

(12)

Echelon F... MORE

(14)

Consistent Systems of Linear Equations

(11)

Applications (Optional)

(7)

Matrix Operations

(15)

Algebraic Properties of Matrix Operations

(10)

Linear Independence and Nonsingular Matrices

(9)

Data Fitting, Numerical Integration, and Numerical Differentiation (Optional)

(12)

Matrix Inverses and Their Properties

(21)

Vectors in 2-Space and 3-Space

113

(50)

Vectors in the Plane

114

(14)

Vectors in Space

128

(7)

The Dot Product and the Cross Product

135

(13)

Lines and Planes in Space

148

(15)

The Vector Space Rn

163

(112)

Introduction

164

(3)

Vector Space Properties of Rn

167

(9)

Examples of Subspaces

176

(12)

Bases for Subspaces

188

(14)

Dimension

202

(12)

Orthogonal Bases for Subspaces

214

(11)

Linear Transformations from Rn to Rm

225

(18)

Least-Squares Solutions to Inconsistent Systems, with Applications to Data Fitting

243

(12)

Theory and Practice of Least Squares

255

(20)

The Eigenvalue Problem

275

(82)

The Eigenvalue Problem for (2 × 2) Matrices

276

(4)

Determinants and the Eigenvalue Problem

280

(10)

Elementary Operations and Determinants (Optional)

290

(8)

Eigenvalues and the Characteristic Polynomial

298

(9)

Eigenvectors and Eigenspaces

307

(8)

Complex Eigenvalues and Eigenvectors

315

(10)

Similarity Transformations and Diagonalization

325

(13)

Difference Equations; Markov Chains; Systems of Differential Equations (Optional)

338

(19)

Vector Spaces and Linear Transformations

357

(90)

Introduction

358

(2)

Vector Spaces

360

(8)

Subspaces

368

(7)

Linear Independence, Bases, and Coordinates

375

(13)

Dimension

388

(4)

Inner-Product Spaces, Orthogonal Bases, and Projections (Optional)

392

(11)

Linear Transformations

403

(8)

Operations with Linear Transformations

411

(8)

Matrix Representations for Linear Transformations

419

(12)

Change of Basis and Diagonalization

431

(16)

Determinants

447

(36)

Introduction

448

(1)

Cofactor Expansions of Determinants

448

(7)

Elementary Operations and Determinants

455

(10)

Cramer's Rule

465

(6)

Applications of Determinants: Inverses and Wronksians

471

(12)

Eigenvalues and Applications

483

Quadratic Forms

484

Systems of Differential Equations

493

Transformation to Hessenberg Form

502

Eigenvalues of Hessenberg Matrices

510

Householder Transformations

519

The QR Factorization and Least-Squares Solutions

531

Matrix Polynomials and the Cayley--Hamilton Theorem

540

Generalized Eigenvectors and Solutions of Systems of Differential Equations

546

Appendix: An Introduction to MATLAB

AP1

Answers to Selected Odd-Numbered Exercises

AN1

Index

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Introduction to Linear Algebra

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