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Linear Algebra and Its Applications,9780201347746
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Linear Algebra and Its Applications

by
Edition:
2nd
ISBN13:

9780201347746

ISBN10:
0201347741
Format:
Hardcover
Pub. Date:
8/1/1999
Publisher(s):
Addison-Wesley
List Price: $114.00

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This is the 2nd edition with a publication date of 8/1/1999.
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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. Finally, when discussed in the abstract, these concepts are more accessible. Students' conceptual understanding is reinforced through True/False questions, practice problems, and the use of technology. David Lay changed the face of linear algebra with the execution of this philosophy, and continues his quest to improve the way linear algebra is taught with the new Updated Second Edition. With this update, he builds on this philosophy through increased visualization in the text, vastly enhanced technology support, and an extensive instructor support package. He has added additional figures to the text to help students visualize abstract concepts at key points in the course. A new dedicated CD and Website further enhance the course materials by providing additional support to help students gain command of difficult concepts. The CD, included in the back of the book, contains a wealth of new materials, with a registration coupon allowing access to a password-protected Website. These new materials are tied directly to the text, providing a comprehensive package for teaching and learning linear algebra.

Table of Contents

Preface xiii
A Note To Students xix
Linear Equations in Linear Algebra
1(96)
Introductory Example: Linear Models in Economics and Engineering
1(96)
Systems of Linear Equations
2(11)
Row Reduction and Echelon Forms
13(14)
Vector Equations
27(12)
The Matrix Equation Ax = b
39(9)
Solution Sets of Linear Systems
48(10)
Linear Independence
58(8)
Introduction to Linear Transformations
66(10)
The Matrix of a Linear Transformation
76(9)
Linear Models in Business, Science, and Engineering
85(10)
Supplementary Exercises
95(2)
Matrix Algebra
97(82)
Introductory Example: Computer Graphics in Automotive Design
97(82)
Matrix Operations
98(12)
The Inverse of a Matrix
110(10)
Characterizations of Invertible Matrices
120(5)
Partitioned Matrices
125(8)
Matrix Factorizations
133(10)
Iterative Solutions of Linear Systems
143(5)
The Leontief Input-Output Model
148(7)
Applications to Computer Graphics
155(10)
Subspaces of Rn
165(12)
Supplementary Exercises
177(2)
Determinants
179(30)
Introductory Example: Determinants in Analytic Geometry
179(30)
Introduction to Determinants
180(7)
Properties of Determinants
187(8)
Cramer's Rule, Volume, and Linear Transformations
195(11)
Supplementary Exercises
206(3)
Vector Spaces
209(86)
Introductory Example: Space Flight and Control Systems
209(86)
Vector Spaces and Subspaces
210(10)
Null Spaces, Column Spaces, and Linear Transformations
220(11)
Linearly Independent Sets; Bases
231(9)
Coordinate Systems
240(10)
The Dimension of a vector Space
250(7)
Rank
257(8)
Change of Basis
265(6)
Applications to Difference Equations
271(11)
Applications to Markov Chains
282(10)
Supplementary Exercises
292(3)
Eigenvalues and Eigenvectors
295(72)
Introductory Example: Dynamical Systems and Spotted Owls
295(72)
Eigenvectors and Eigenvalues
296(9)
The Characteristic Equation
305(8)
Diagonalization
313(8)
Eigenvectors and Linear Transformations
321(8)
Complex Eigenvalues
329(7)
Discrete Dynamical Systems
336(11)
Applications to Differential Equations
347(10)
Iterative Estimates for Eigenvalues
357(8)
Supplementary Exercises
365(2)
Orthogonality and Least-Squares
367(74)
Introductory Example: Readjusting the North American Datum
367(74)
Inner Product, Length, and Orthogonality
369(9)
Orthogonal Sets
378(11)
Orthogonal Projections
389(8)
The Gram-Schmidt Process
397(7)
Least-Squares Problems
404(10)
Applications to Linear Models
414(8)
Inner Product Spaces
422(9)
Applications of Inner Product Spaces
431(8)
Supplementary Exercises
439(2)
Symmetric Matrices and Quadratic Forms
441
Introductory Example: Multichannel Image Processing
441
Diagonalization of Symmetric Matrices
443
Quadratic Forms
450
Constrained Optimization
458
The Singular Value Decomposition
466
Applications to Image Processing and Statistics
477
Supplementary Exercises
485
Appendixes
A Uniqueness of the Reduced Echelon Form
A1
B Complex Numbers
A3
Glossary A9
Answers to Odd-Numbered Exercises A21
Index I1


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