Pearson - Linear Algebra and Its Applications, 4/E

In this section:

Description

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rⁿ setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

Features

Fundamental ideas of linear algebra are introduced within the first seven lectures, in the concrete setting of Rⁿ, and then gradually examined from different points of view. Later generalizations of these concepts appear as natural extensions of familiar ideas.
Focus on visualization of concepts throughout the book helps readers grasp the concepts.
Icons in the margins to flag topics for which expanded or enhanced material is available on the textbook’s companion Website..
A modern view of matrix multiplication is presented, with definitions and proofs focusing on the columns of a matrix rather than on the matrix entries.
Numerical Notes give a realistic flavor to the text. Students are reminded frequently of issues that arise in the real-life use of linear algebra.
Each major concept in the course is given a geometric interpretation because many students learn better when they can visualize an idea.
[M] exercises appear in every section. To be solved with the aid of a [M]atrix program such as MATLAB^™, Maple^®, Mathematica^®, MathCad^®, Derive^® or programmable calculators with matrix capabilities, such as the TI-83 Plus^®, TI-86^®, TI-89^®, and HP-48G^®. Data for these exercises are provided on the Web.

New To This Edition

More than 25% of the exercises are new or updated, especially the computational exercises. The exercise sets remain one of the most important features of this book. They are crafted in a way that retells the substance of each of the sections they follow, developing the students’ confidence while challenging them to practice and generalize the new ideas they have just encountered.
25% of chapter openers are new, providing applications of linear algebra and the motivation for developing the mathematics that follows.
Chapter 8, The Geometry of Vector Spaces, has been added to the text. Sections include Affine Combinations, Affine Independence, Convex Combinations, Hyperplanes, Polytopes, and Curves and Surfaces.
The Study Guide has been updated to cover the new Chapter 8. As with past editions, the Study Guide incorporates detailed solutions to every third odd-numbered exercise, as well as solutions to every odd-numbered writing exercise for which the main text only provides a hint.
A new chapter–Chapter 10: Finite-State Markov Chains–is now available online.
PowerPoint^® slides are now available for 25 core sections of the text. 75 figures from the text are also available for as PowerPoint slides.

Table of Contents

1. Linear Equations in Linear Algebra

Introductory Example: Linear Models in Economics and Engineering

1.1 Systems of Linear Equations

1.2 Row Reduction and Echelon Forms

1.3 Vector Equations

1.4 The Matrix Equation Ax = b

1.5 Solution Sets of Linear Systems

1.6 Applications of Linear Systems

1.7 Linear Independence

1.8 Introduction to Linear Transformations

1.9 The Matrix of a Linear Transformation

1.10 Linear Models in Business, Science, and Engineering

Supplementary Exercises

2. Matrix Algebra

Introductory Example: Computer Models in Aircraft Design

2.1 Matrix Operations

2.2 The Inverse of a Matrix

2.3 Characterizations of Invertible Matrices

2.4 Partitioned Matrices

2.5 Matrix Factorizations

2.6 The Leontief Input—Output Model

2.7 Applications to Computer Graphics

2.8 Subspaces of Rⁿ

2.9 Dimension and Rank

Supplementary Exercises

3. Determinants

Introductory Example: Random Paths and Distortion

3.1 Introduction to Determinants

3.2 Properties of Determinants

3.3 Cramer’s Rule, Volume, and Linear Transformations

Supplementary Exercises

4. Vector Spaces

Introductory Example: Space Flight and Control Systems

4.1 Vector Spaces and Subspaces

4.2 Null Spaces, Column Spaces, and Linear Transformations

4.3 Linearly Independent Sets; Bases

4.4 Coordinate Systems

4.5 The Dimension of a Vector Space

4.6 Rank

4.7 Change of Basis

4.8 Applications to Difference Equations

4.9 Applications to Markov Chains

Supplementary Exercises

5. Eigenvalues and Eigenvectors

Introductory Example: Dynamical Systems and Spotted Owls

5.1 Eigenvectors and Eigenvalues

5.2 The Characteristic Equation

5.3 Diagonalization

5.4 Eigenvectors and Linear Transformations

5.5 Complex Eigenvalues

5.6 Discrete Dynamical Systems

5.7 Applications to Differential Equations

5.8 Iterative Estimates for Eigenvalues

Supplementary Exercises

6. Orthogonality and Least Squares

Introductory Example: Readjusting the North American Datum

6.1 Inner Product, Length, and Orthogonality

6.2 Orthogonal Sets

6.3 Orthogonal Projections

6.4 The Gram—Schmidt Process

6.5 Least-Squares Problems

6.6 Applications to Linear Models

6.7 Inner Product Spaces

6.8 Applications of Inner Product Spaces

Supplementary Exercises

7. Symmetric Matrices and Quadratic Forms

Introductory Example: Multichannel Image Processing

7.1 Diagonalization of Symmetric Matrices

7.2 Quadratic Forms

7.3 Constrained Optimization

7.4 The Singular Value Decomposition

7.5 Applications to Image Processing and Statistics

Supplementary Exercises

8. The Geometry of Vector Spaces

Introductory Example: The Platonic Solids

8.1 Affine Combinations

8.2 Affine Independence

8.3 Convex Combinations

8.4 Hyperplanes

8.5 Polytopes

8.6 Curves and Surfaces

9. Optimization (Online Only)

Introductory Example: The Berlin Airlift

9.1 Matrix Games

9.2 Linear Programming–Geometric Method

9.3 Linear Programming–Simplex Method

9.4 Duality

10. Finite-State Markov Chains (Online Only)

Introductory Example: Google and Markov Chains

10.1 Introduction and Examples

10.2 The Steady-State Vector and Google's PageRank

10.3 Finite-State Markov Chains

10.4 Classification of States and Periodicity

10.5 The Fundamental Matrix

10.6 Markov Chains and Baseball Statistics

Appendices

A. Uniqueness of the Reduced Echelon Form

B. Complex Numbers

Courses

Introductory Linear Algebra (Mathematics)

Previous Edition(s)

Linear Algebra and Its Applications with CD-ROM, Update, 3/E
Lay
©2006 | Pearson | Cloth Bound w/CD-ROM; 576 pp | Out of Print
ISBN-10: 0321287134 | ISBN-13: 9780321287137
Brief Description |
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

More Info
Linear Algebra and Its Applications with CD-ROM, Update, 3/E
Lay
©2006 | Pearson | Cloth Bound w/CD-ROM; 576 pp | Out of Print
ISBN-10: 0321287134 | ISBN-13: 9780321287137
Brief Description |
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

More Info
Linear Algebra and Its Applications with CD-ROM, Update, 3/E
Lay
©2006 | Pearson | Cloth Bound w/CD-ROM; 576 pp | Out of Print
ISBN-10: 0321287134 | ISBN-13: 9780321287137
Brief Description |
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.

More Info

In this section:

Author Bios

Author Bios

David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.

As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter.

Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or University Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.

Websites and Online Courses

In this section:

Websites and Online Courses

Companion Website for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Website | Live
ISBN-10: 0321780736 | ISBN-13: 9780321780737
More Info

In this section:

Instructor Resources

Downloadable Instructor Resources
Other Instructor Resources

Student Resources

Websites and online courses
Other student resources

eLearning & Assessment

Websites and Online Courses

Course & Discipline Resources

For Introductory Linear Algebra
For the Mathematics Discipline

Chapter 10: "Finite-State Markov Chains" (online only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321798961 | ISBN-13: 9780321798961

Chapter 9: "Optimatization" (online only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321798953 | ISBN-13: 9780321798954

Instructor's Maple Manual (Download only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321756053 | ISBN-13: 9780321756053

Instructor's Solutions Manual for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Paper; 425 pp | Instock
ISBN-10: 0321388887 | ISBN-13: 9780321388889

Mathematica Manual (Download only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321388852 | ISBN-13: 9780321388858

Online MATLAB Manual for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321533658 | ISBN-13: 9780321533654

PowerPoint Slides (Download only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321758064 | ISBN-13: 9780321758064

TI-83+/86/89 Manual (Download only) for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321388879 | ISBN-13: 9780321388872

TestGen® Computerized Test Bank for Linear Algebra and its Applications, 4/E
Lay
©2012 | Pearson | On-line Supplement | Live
ISBN-10: 0321388895 | ISBN-13: 9780321388896

Websites and online courses

Instructor's Edition for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Cloth; 656 pp | Instock
ISBN-10: 0321385187 | ISBN-13: 9780321385185
More Info

Companion Website for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Website | Live
ISBN-10: 0321780736 | ISBN-13: 9780321780737
More Info

Companion Website for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Website | Live
ISBN-10: 0321780736 | ISBN-13: 9780321780737
More Info

Other student resources

Student Study Guide for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Paper; 450 pp | Instock
ISBN-10: 0321388836 | ISBN-13: 9780321388834
Net price: $27.50 (What's this?)More Info

For Introductory Linear Algebra

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
Suggested retail price: $88.00Net price: $66.00 (What's this?)More Info

Understanding Linear Algebra Using MATLAB
Kleinfeld & Kleinfeld
©2001 | Pearson | Paper; 210 pp | Out of Stock
ISBN-10: 0130609455 | ISBN-13: 9780130609458
Suggested retail price: $38.60Net price: $28.95 (What's this?)More Info

Visualizing Linear Algebra Using Maple
Keith
©2001 | Pearson | Paper; 250 pp | Instock
ISBN-10: 0130418161 | ISBN-13: 9780130418166
Suggested retail price: $38.60Net price: $28.95 (What's this?)More Info

For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006 | Pearson | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
Net price: $3.00 (What's this?)More Info

Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
Net price: $3.00 (What's this?)More Info

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
ISBN-10: 0321517199 | ISBN-13: 9780321517197
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586
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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
Net price: $35.85 (What's this?)More Info

Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
Net price: $10.00 (What's this?)More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Pearson | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
Net price: $27.50 (What's this?)More Info

Prealgebra Review Workbook
Wheel
©2006 | Pearson | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
Net price: $27.50 (What's this?)More Info

Review of Algebra, A
Howard
©2002 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
Net price: $27.50 (What's this?)More Info

Spanish Basic Math Study Card
Leonarte
©2007 | Pearson | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
Net price: $3.00 (What's this?)More Info

TestGen All-in-One 2005 Package
Addison-Wesley
©2005 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321334469 | ISBN-13: 9780321334466
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Websites and Online Courses

Companion Website for Linear Algebra and Its Applications, 4/E
Lay
©2012 | Pearson | Website | Live
ISBN-10: 0321780736 | ISBN-13: 9780321780737
More Info

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Linear Algebra and Its Applications, Books a la Carte Edition, 4/E
Lay
©2012 | Pearson | Unbound (Saleable); 624 pp | Instock
ISBN-10: 0321780728 | ISBN-13: 9780321780720
Net price: $68.40 (What's this?)Brief Description |
This edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value—this format costs significantly less than a new textbook.

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. David Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
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Linear Algebra and Its Applications, Books a la Carte edition plus MyMathLab Access Code Card
Lay
©2012 | Pearson | Paper Package | Instock
ISBN-10: 0321836146 | ISBN-13: 9780321836144
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Linear Algebra and Its Applications, CourseSmart eTextbook, 4/E
Lay
©2012 | Pearson | Electronic Book | Available
ISBN-10: 0321780213 | ISBN-13: 9780321780218
Online purchase price: $60.99Brief Description |
CourseSmart Textbooks Online is an exciting new choice for students looking to save money. As an alternative to purchasing the print textbook, students can subscribe to the same content online and save up to 50% off the suggested list price of the print text. With a CourseSmart etextbook, students can search the text, make notes online, print out reading assignments that incorporate lecture notes, and bookmark important passages for later review. For more information, or to subscribe to the CourseSmart eTextbook, visit www.coursesmart.com.
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