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Linear Algebra and Its Applications with CD-ROM, Update,9780321287137
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Linear Algebra and Its Applications with CD-ROM, Update

by
Edition:
3rd
ISBN13:

9780321287137

ISBN10:
0321287134
Format:
Hardcover w/CD
Pub. Date:
1/1/2006
Publisher(s):
Addison Wesley
Includes 2-weeks free access to
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Summary

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.

Table of Contents

Preface ix
A Note to Students xv
Linear Equations in Linear Algebra
1(104)
Introductory Example: Linear Models in Economics and Engineering
1(104)
Systems of Linear Equations
2(12)
Row Reduction and Echelon Forms
14(14)
Vector Equations
28(12)
The Matrix Equation Ax = b
40(10)
Solution Sets of Linear Systems
50(7)
Applications of Linear Systems
57(8)
Linear Independence
65(8)
Introduction to Linear Transformations
73(9)
The Matrix of a Linear Transformation
82(10)
Linear Models in Business, Science, and Engineering
92(10)
Supplementary Exercises
102(3)
Matrix Algebra
105(80)
Introductory Example: Computer Models in Aircraft Design
105(80)
Matrix Operations
107(11)
The Inverse of a Matrix
118(10)
Characterizations of Invertible Matrices
128(6)
Partitioned Matrices
134(8)
Matrix Factorizations
142(10)
The Leontief Input-Output Model
152(6)
Applications to Computer Graphics
158(9)
Subspaces of Rn
167(9)
Dimension and Rank
176(7)
Supplementary Exercises
183(2)
Determinants
185(30)
Introductory Example: Determinants in Analytic Geometry
185(30)
Introduction to Determinants
186(6)
Properties of Determinants
192(9)
Cramer's Rule, Volume, and Linear Transformations
201(10)
Supplementary Exercises
211(4)
Vector Spaces
215(86)
Introductory Example: Space Flight and Control Systems
215(86)
Vector Spaces and Subspaces
216(10)
Null Spaces, Column Spaces, and Linear Transformations
226(11)
Linearly Independent Sets: Bases
237(9)
Coordinate Systems
246(10)
The Dimension of a Vector Space
256(6)
Rank
262(9)
Change of Basis
271(6)
Applications to Difference Equations
277(11)
Applications to Markov Chains
288(10)
Supplementary Exercises
298(3)
Eigenvalues and Eigenvectors
301(72)
Introductory Example: Dynamical Systems and Spotted Owls
301(72)
Eigenvectors and Eigenvalues
302(8)
The Characteristic Equation
310(9)
Diagonalization
319(8)
Eigenvectors and Linear Transformations
327(8)
Complex Eigenvalues
335(7)
Discrete Dynamical Systems
342(11)
Applications to Differential Equations
353(10)
Iterative Estimates for Eigenvalues
363(7)
Supplementary Exercises
370(3)
Orthogonality and Least Squares
373(74)
Introductory Example: Readjusting the North American Datum
373(74)
Inner Product, Length, and Orthogonality
375(9)
Orthogonal Sets
384(10)
Orthogonal Projections
394(8)
The Gram--Schmidt Process
402(7)
Least-Squares Problems
409(10)
Applications to Linear Models
419(8)
Inner Product Spaces
427(9)
Applications of Inner Product Spaces
436(8)
Supplementary Exercises
444(3)
Symmetric Matrices and Quadratic Forms
447
Introductory Example: Multichannel Image Processing
447
Diagonalization of Symmetric Matrices
449(6)
Quadratic Forms
455(8)
Constrained Optimization
463(8)
The Singular Value Decomposition
471(11)
Applications to Image Processing and Statistics
482(9)
Supplementary Exercises
491
The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
Affine Combinations
Affine Independence
Convex Combinations
Hyperplanes
Polytopes
Curves and Surfaces
Optimization
Introductory Example: The Berlin Airlift
Matrix Games
Linear Programming---Geometric Method
Linear Programming---Simplex Method
Duality
Appendixes
A Uniqueness of the Reduced Echelon Form
1(2)
B Complex Numbers
3(6)
Glossary 9(10)
Answers to Odd-Numbered Exercises 19
Index 1


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