Linear Algebra and Its Applications Updated

Linear Algebra and Its Applications Updated

by HEPC Inc. Staff

Paperback

$74.33

Product Details

ISBN-13: 9780201648454
Publisher: Addison-Wesley
Publication date: 08/28/1999
Pages: 640
Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

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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