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Linear algebra and its applications

Author: Lay, David C. Publisher: Addison Wesley, 1994.Language: EnglishDescription: 445 p. : Graphs/Ill. ; 24 cm.ISBN: 0201520311Type of document: Book Bibliography/Index:
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA303 .L39 1994
(Browse shelf)
32419001193022
Available 32419001193022
Total holds: 0

Digitized

Linear Algebra and Its Applications Contents PREFACE ix A NOTE TO STUDENTS xvi I SYSTEMS OF LINEAR EQUATIONS / Introductory Example: Linear Models in Economics and Engineering / 1.1 Introduction to Systems of Linear Equations 1.2 Row Reduction and Echelon Forms 1.3 Applications of Linear Systems 13 25 2 Supplementary Exercises 34 2 VECTOR AND MATRIX EQUATIONS 37 Introductory Example: Nutrition Problems 37 2.1 Vectors in R" 38 48 2.2 The Equation Ax = b 2.3 Solution Sets of Linear Systems 56 2.4 Linear Independence 63 2.5 Introduction to Linear Transformations 7/ 2.6 The Matrix of a Linear Transformation 79 2.7 Applications to Nutrition and Population Movement 85 Supplementary Exercises 92 3 MATRIX ALGEBRA 95 Introductory Example: Computer Graphics in Automotive Design 3.1 Matrix Operations 95 96 3.2 The Inverse of a Matrix 107 3.3 Characterizations of Invertible Matrices 116 3.4 Partitioned Matrices 121 3.5 Matrix Factorizations 128 3.6 Iterative Solutions of Linear Systems 137 3.7 The Leontief Input--Output Model 3.8 Applications to Computer Graphics Supplementary Exercises 158 142 148 4 DETERMINANTS 161 Introductory Example: Determinants in Analytic Geometry 4.1 Introduction to Determinants 162 4.2 Properties of Determinants 168 4.3 Cramer's Rule, Volume, and Linear Transformations Supplementary Exercises 186 161 176 5 VECTOR SPACES 189 Introductory Example: Space Flight and Control Systems 189 5.1 Vector Spaces and Subspaces 190 5.2 Null Spaces, Column Spaces, and Linear Transformations 200 5.3 Linearly Independent Sets; Bases 211 5.4 Coordinate Systems 219 5.5 The Dimension of a Vector Space 229 5.6 Rank 235 5.7 Change of Basis 243 5.8 Applications to Difference Equations 248 5.9 Applications to Markov Chains 259 Supplementary Exercises 269 6 EIGENVALUES AND EIGENVECTORS 271 Introductory Example: Dynamical Systems and Spotted Owls 6.1 Eigenvectors and Eigenvalues 273 6.2 The Characteristic Equation 280 6.3 Diagonalization 288 6.4 Eigenvectors and Linear Transformations 6.5 Complex Eigenvalues 303 6.6 Applications to Dynamical Systems 6.7 Iterative Estimates for Eigenvalues Supplementary Exercises 329 271 296 310 321 7 ORTHOGONALITY AND LEAST-SQUARES 331 Introductory Example: Readjusting the North American Datum 7.1 Inner Product, Length, and Orthogonality 7.2 Orthogonal Sets 342 7.3 Orthogonal Projections 352 7.4 The Gram­Schmidt Process 359 7.5 Least-Squares Problems 366 7.6 Applications to Linear Models 376 333 331 7.7 Inner Product Spaces 384 7.8 Applications of Inner Product Spaces Supplementary Exercises 401 393 8 SYMMETRIC MATRICES AND QUADRATIC FORMS 403 Introductory Example: Multichannel Image Processing 403 8.1 Diagonalization of Symmetric Matrices 405 8.2 Quadratic Forms 411 8.3 Constrained Optimization 419 8.4 The Singular Value Decomposition 426 8.5 Applications to Image Processing and Statistics 435 Supplementary Exercises 444 APPENDICES A Uniqueness of the Reduced Echelon Form B Complex Numbers A-3 A-1 GLOSSARY A-9 ANSWERS TO ODD-NUMBERED EXERCISES A-21

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