Description

Features

New To This Edition

1. New Section on Matrix Arithmetic

One of the longer sections in the previous edition was the section on matrix algebra in Chapter 1. The material in that section has been expanded further for the current edition. Rather than include an overly long revised section, we have divided the material into sections titled Matrix Arithmetic and Matrix Algebra.

2. New Exercises

After seven editions it was quite a challenge to come up with additional original exercises. This eighth edition has more than 130 new exercises. The new exercises are not evenly distributed throughout the book. Some sections have many new exercises and others have few or none.

3. New Subsections and Applications

A new subsection on cross products has been included in Section 3 of Chapter 2. A new application to Newtonian Mechanics has also been added to that section. In Section 4 of Chapter 6 (Hermitian Matrices), a new subsection on the Real Schur Decomposition has been added.

4. New and Improved Notation

The standard notation for the jth column vector of a matrix A is a_j , however, there seems to be no universally accepted notation for row vectors. In the MATLAB package, the ith row of A is denoted by A(i, :). In previous editions of this book we used a similar notation a(i, :), however, this notation seems somewhat artificial. For this edition we use the same notations as for a column vector except we put a horizontal arrow above the letter to indicate that the vector is a row vector (an horizontal array) rather than a column vector (a vertical array).

We have also introduced improved notation for the standard Euclidean vector spaces and their complex counterparts.

5. Other Revisions

Various other revisions have been made throughout the text. Many of these revisions were suggested by reviewers.

6. Special Web Site and Supplemental Web Materials

Pearson has developed a special Web site to accompany the 8th edition. This site includes a host of materials for both students and instructors.

Table of Contents

Preface

What’s New in the Eighth Edition?

Computer Exercises

Overview of Text

Suggested Course Outlines

Supplementary Materials

Acknowledgments

1. Matrices and Systems of Equations

1.1 Systems of Linear Equations

1.2 Row Echelon Form

1.3 Matrix Arithmetic

1.4 Matrix Algebra

1.5 Elementary Matrices

1.6 Partitioned Matrices

            Matlab Exercises

            Chapter Test A

            Chapter Test B

2. Determinants

2.1 The Determinant of a Matrix

2.2 Properties of Determinants

2.3 Additional Topics and Applications

            Matlab Exercises

            Chapter Test A

            Chapter Test B

3. Vector Spaces

3.1 Definition and Examples

3.2 Subspaces

3.3 Linear Independence

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space and Column Space

            Matlab Exercises

            Chapter Test A

            Chapter Test B

4. Linear Transformations

4.1 Definition and Examples

4.2 Matrix Representations of Linear Transformations

4.3 Similarity

            Matlab Exercises

            Chapter Test A

            Chapter Test B

5. Orthogonality

5.1 The Scalar Product in Rⁿ

5.2 Orthogonal Subspaces

5.3 Least Squares Problems

5.4 Inner Product Spaces

5.5 Orthonormal Sets

5.6 The Gram—Schmidt Orthogonalization Process

5.7 Orthogonal Polynomials

            Matlab Exercises

            Chapter Test A

            Chapter Test B

6. Eigenvalues

6.1 Eigenvalues and Eigenvectors

6.2 Systems of Linear Differential Equations

6.3 Diagonalization

6.4 Hermitian Matrices

6.5 The Singular Value Decomposition

6.6 Quadratic Forms

6.7 Positive Definite Matrices

6.8 Nonnegative Matrices

            Matlab Exercises

            Chapter Test A

            Chapter Test B

7. Numerical Linear Algebra

7.1 Floating-Point Numbers

7.2 Gaussian Elimination

7.3 Pivoting Strategies

7.4 Matrix Norms and Condition Numbers

7.5 Orthogonal Transformations

7.6 The Eigenvalue Problem

7.7 Least Squares Problems

            Matlab Exercises

            Chapter Test A

            Chapter Test B

Appendix: MATLAB

The MATLAB Desktop Display

Basic Data Elements

Submatrices

Generating Matrices

Matrix Arithmetic

MATLAB Functions

Programming Features

M-files

Relational and Logical Operators

Columnwise Array Operators

Graphics

Symbolic Toolbox

Help Facility

Conclusions

Bibliography

A. Linear Algebra and Matrix Theory

B. Applied and Numerical Linear Algebra

C. Books of Related Interest

Courses

Introductory Linear Algebra  (Mathematics)

Previous Edition(s)

• Linear Algebra with Applications, 7/E
  Leon
  ©2006  |  Pearson  |  Cloth; 544 pp  |  Out of Print
  ISBN-10: 0131857851  |  ISBN-13: 9780131857858
    Brief Description  | 

  

  For sophomore-level or junior/senior-level first courses in Linear Algebra; assumes a Calculus prerequisite.

   

  This thorough and accessible text – from one of the leading figures in the use of technology in linear algebra – gives students a challenging and broad understanding of the subject.  The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests.  The book stresses the important role geometry and visualization play in understanding linear algebra.  This edition will continue to be packaged with the ancillary ATLAST computer exercise guide, as well as new MATLAB and Maple guides, which are also free in the package.

  More Info
  

Author Bios

Steven J. Leon is a Chancellor Professor of Mathematics at the University of Massachusetts Dartmouth. He has been a Visiting Professor at Stanford University, ETH Zurich (the Swiss Federal Institute of Technology), KTH (the Royal Institute of Technology in Stockholm), UC San Diego, and Brown University. His areas of specialty are linear algebra and numerical analysis.

Leon is currently serving as Chair of the Education Committee of the International Linear Algebra Society and as Contributing Editor to Image, the Bulletin of the International Linear Algebra Society. He had previously served as Editor-in-Chief of Image from 1989 to 1997. In the 1990’s he also served as Director of the NSF sponsored ATLAST Project (Augmenting the Teaching of Linear Algebra using Software Tools). The project conducted 18 regional faculty workshops during the period from 1992–1997.

Backcover Copy

Companion Website for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Website  |  Live
ISBN-10: 0136009328  |  ISBN-13: 9780136009320
This online resource is available at no cost at http://www.pearsonhighered.com/leon.
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Downloadable Instructor Resources

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Instructor's Solutions Manual for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Paper; 168 pp  |  Out of Stock
ISBN-10: 013600931X  |  ISBN-13: 9780136009313

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Companion Website for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Website  |  Live
ISBN-10: 0136009328  |  ISBN-13: 9780136009320
This online resource is available at no cost at http://www.pearsonhighered.com/leon.
More Info

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Companion Website for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Website  |  Live
ISBN-10: 0136009328  |  ISBN-13: 9780136009320
This online resource is available at no cost at http://www.pearsonhighered.com/leon.
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Student Study Guide for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Paper; 415 pp  |  Instock
ISBN-10: 0136009301  |  ISBN-13: 9780136009306
Suggested retail price:  $36.67    Buy from myPearsonStoreNet price: $27.50  (What's this?)More Info

ATLAST Manual, 2/E
Leon
©2003  |  Pearson  |  Paper; 270 pp  |  Instock
ISBN-10: 0131011219  |  ISBN-13: 9780131011212
Suggested retail price:  $37.40Net price: $28.05  (What's this?)More Info

Linear Algebra Labs with MATLAB, 3/E
Hill & Zitarelli
©2004  |  Pearson  |  Paper; 336 pp  |  Instock
ISBN-10: 0131432745  |  ISBN-13: 9780131432741
Suggested retail price:  $38.60Net price: $28.95  (What's this?)More Info

Maple Supplement for Linear Algebra, A
Maloney
©2005  |  Pearson  |  Paper; 192 pp  |  Instock
ISBN-10: 0131453378  |  ISBN-13: 9780131453371
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Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001  |  Pearson  |  Paper; 210 pp  |  Out of Stock
ISBN-10: 0130609455  |  ISBN-13: 9780130609458
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Visualizing Linear Algebra Using Maple
Keith
©2001  |  Pearson  |  Paper; 250 pp  |  Instock
ISBN-10: 0130418161  |  ISBN-13: 9780130418166
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Allied Health Study Card, 2/E
Forshier
©2006  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321394747  |  ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006  |  Pearson  |  Study Card; 6 pp  |  Instock
ISBN-10: 0321394763  |  ISBN-13: 9780321394767
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Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000  |  Pearson  |  Unknown / Other  |  Instock
ISBN-10: 0201716275  |  ISBN-13: 9780201716276
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Concept Videos: Algebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
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Addison-Wesley
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Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997  |  Pearson  |  Paper; 195 pp  |  Instock
ISBN-10: 0136492037  |  ISBN-13: 9780136492030
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321357744  |  ISBN-13: 9780321357748
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
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Prealgebra Review Workbook
Wheel
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ISBN-10: 0321473329  |  ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002  |  Pearson  |  Paper; 224 pp  |  Instock
ISBN-10: 0201773473  |  ISBN-13: 9780201773477
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Spanish Basic Math Study Card
Leonarte
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TestGen All-in-One 2005 Package
Addison-Wesley
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ISBN-10: 0321334469  |  ISBN-13: 9780321334466
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Companion Website for Linear Algebra with Applications, 8/E
Leon
©2010  |  Pearson  |  Website  |  Live
ISBN-10: 0136009328  |  ISBN-13: 9780136009320
This online resource is available at no cost at http://www.pearsonhighered.com/leon.
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• Linear Algebra with Applications, Books a la Carte Edition, 8/E
  Leon
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• Linear Algebra with Applications, CourseSmart eTextbook, 8/E
  Leon
  ©2010  |  Pearson  |  Electronic Book; 552 pp  |  Available
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