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Linear Algebra : A Modern Introduction,9780534998455
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Linear Algebra : A Modern Introduction

by
Edition:
2nd
ISBN13:

9780534998455

ISBN10:
0534998453
Format:
Hardcover
Pub. Date:
1/24/2005
Publisher(s):
Cengage Learning
List Price: $317.99

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Summary

David Poole's innovative book emphasizes vectors and geometric intuition from the start and better prepares students to make the transition from the computational aspects of the course to the theoretical. Poole covers vectors and vector geometry first to enable students to visualize the mathematics while they are doing matrix operations. With a concrete understanding of vector geometry, students are able to visualize and understand the meaning of the calculations that they will encounter. By seeing the mathematics and understanding the underlying geometry, students develop mathematical maturity and can think abstractly when they reach vector spaces. Throughout the text, Poole's direct conversational writing style connects with students, and an abundant selection of applications from a broad range of disciplines clearly demonstrates the relevance of linear algebra.

Table of Contents

Preface vii
To the Instructor xvii
To the Student xxiii
Vectors
1(57)
Introduction: The Racetrack Game
1(2)
The Geometry and Algebra of Vectors
3(12)
Length and Angle: The Dot Product
15(16)
Exploration: Vectors and Geometry
29(2)
Lines and Planes
31(16)
Exploration: The Cross Product
45(2)
Code Vectors and Modular Arithmetic
47(11)
Vignette: The Codabar System
55(1)
Chapter Review
56(2)
Systems of Linear Equations
58(76)
Introduction: Triviality
58(1)
Introduction to Systems of Linear Equations
59(9)
Exploration: Lies My Computer Told Me
66(2)
Direct Methods for Solving Linear Systems
68(22)
Exploration: Partial Pivoting
86(1)
Exploration: Counting Operations: An Introduction to the Analysis of Algorithms
87(3)
Spanning Sets and Linear Independence
90(11)
Applications
101(21)
Allocation of Resources
101(2)
Balancing Chemical Equations
103(1)
Network Analysis
104(2)
Electrical Networks
106(3)
Finite Linear Games
109(10)
Vignette: The Global Positioning System
119(3)
Iterative Methods for Solving Linear Systems
122(12)
Chapter Review
132(2)
Matrices
134(118)
Introduction: Matrices in Action
134(2)
Matrix Operations
136(16)
Matrix Algebra
152(9)
The Inverse of a Matrix
161(17)
The LU Factorization
178(11)
Subspaces, Basis, Dimension, and Rank
189(20)
Introduction to Linear Transformations
209(19)
Vignette: Robotics
224(4)
Applications
228(24)
Markov Chains
228(5)
Population Growth
233(2)
Graphs and Digraphs
235(5)
Error-Correcting Codes
240(10)
Chapter Review
250(2)
Eigenvalues and Eigenvectors
252(111)
Introduction: A Dynamical System on Graphs
252(1)
Introduction to Eigenvalues and Eigenvectors
253(9)
Determinants
262(27)
Exploration: Geometric Applications of Determinants
283(6)
Eigenvalues and Eigenvectors of nxn Matrices
289(9)
Similarity and Diagonalization
298(10)
Iterative Methods for Computing Eigenvalues
308(14)
Applications and the Perron-Frobenius Theorem
322(41)
Markov Chains
322(5)
Population Growth
327(2)
The Perron-Frobenius Theorem
329(3)
Linear Recurrence Relations
332(5)
Systems of Linear Differential Equations
337(8)
Discrete Linear Dynamical Systems
345(8)
Vignette: Ranking Sports Teams and Searching the Internet
353(8)
Chapter Review
361(2)
Orthogonality
363(68)
Introduction: Shadows on a Wall
363(2)
Orthogonality in Rn
365(10)
Orthogonal Complements and Orthogonal Projections
375(10)
The Gram-Schmidt Process and the QR Factorization
385(12)
Exploration: The Modified QR Factorization
393(2)
Exploration: Approximating Eigenvalues with the QR Algorithm
395(2)
Orthogonal Diagonalization of Symmetric Matrices
397(8)
Applications
405(26)
Dual Codes
405(6)
Quadratic Forms
411(7)
Graphing Quadratic Equations
418(11)
Chapter Review
429(2)
Vector Spaces
431(107)
Introduction: Fibonacci in (Vector) Space
431(2)
Vector Spaces and Subspaces
433(14)
Linear Independence, Basis, and Dimension
447(20)
Exploration: Magic Squares
464(3)
Change of Basis
467(9)
Linear Transformations
476(9)
The Kernel and Range of a Linear Transformation
485(16)
The Matrix of a Linear Transformation
501(21)
Exploration: Tilings, Lattices, and the Crystallographic Restriction
519(3)
Applications
522(16)
Homogeneous Linear Differential Equations
522(7)
Linear Codes
529(7)
Chapter Review
536(2)
Distance and Approximation
538(96)
Introduction: Taxicab Geometry
538(2)
Inner Product Spaces
540(21)
Exploration: Vectors and Matrices with Complex Entries
552(4)
Exploration: Geometric Inequalities and Optimization Problems
556(5)
Norms and Distance Functions
561(16)
Least Squares Approximation
577(22)
The Singular Value Decomposition
599(20)
Vignette: Digital Image Compression
616(3)
Applications
619(15)
Approximation of Functions
619(7)
Error-Correcting Codes
626(5)
Chapter Review
631(3)
Appendix A Mathematical Notation and Methods of Proof 634(9)
Appendix B Mathematical Induction 643(7)
Appendix C Complex Numbers 650(11)
Appendix D Polynomials 661(10)
Answers to Selected Odd-Numbered Exercises 671(35)
Index 706


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