Linear Algebra & Its Applications : Custom Edition for the Univeristy of Buffalo

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Linear Algebra & Its Applications : Custom Edition for the Univeristy of Buffalo

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  • 製本 Hardcover:ハードカバー版/ページ数 492 p.
  • 言語 ENG
  • 商品コード 9780536827227
  • DDC分類 512

Table of Contents

Preface                                            ix
A Note to Students xv
Linear Equations in Linear Algebra 1 (104)
Introductory Example: Linear Models in 1 (1)
Economics and Engineering
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 92 (13)
Engineering
Supplementary Exercises 102(3)
Matrix Algebra 105(80)
Introductory Example: Computer Models in 105(2)
Aircraft Design
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 R'' 167(9)
Dimension and Rank 176(9)
Supplementary Exercises 183(2)
Determinants 185(30)
Introductory Example: Determinants in 185(1)
Analytic Geometry
Introduction to Determinants 186(6)
Properties of Determinants 192(9)
Cramer's Rule, Volume, and Linear 201(14)
Transformations
Supplementary Exercises 211(4)
Vector Spaces 215(86)
Introductory Example: Space Flight and 215(1)
Control Systems
Vector Spaces and Subspaces 216(10)
Null Spaces, Column Spaces, and Linear 226(11)
Transformations
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(13)
Supplementary Exercises 298(3)
Eigenvalues and Eigenvectors 301(72)
Introductory Example: Dynamical Systems 301(1)
and Spotted Owls
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(10)
Supplementary Exercises 370(3)
Orthogonality and Least Squares 373(74)
Introductory Example: Readjusting the 373(2)
North American Datum
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(11)
Supplementary Exercises 444(3)
Symmetric Matrices and Quadratic Forms 447
Introductory Example: Multichannel Image 447(2)
Processing
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 482
Statistics
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