Linear Algebra and its Applications
Publisher: Pearson
Published: 2012
Language: eng
ISBN-13: 9781256144380
Table of contents: title: Preface
pagenum: ix; title: A Note to Students
pagenum: xv; label: Chapter 1
title: Linear Equations in Linear Algebra
pagenum: 1; title: Introductory Example: Linear Models in Economics and Engineering
pagenum: 1; label: 1.1
title: Systems of Linear Equations
pagenum: 2; label: 1.2
title: Row Reduction and Echelon Forms
pagenum: 12; label: 1.3
title: Vector Equations
pagenum: 24; label: 1.4
title: The Matrix Equation \(Ax = b\)
pagenum: 34; label: 1.5
title: Solution Sets of Linear Systems
pagenum: 43; label: 1.6
title: Applications of Linear Systems
pagenum: 49; label: 1.7
title: Linear Independence
pagenum: 55; label: 1.8
title: Introduction to Linear Transformations
pagenum: 62; label: 1.9
title: The Matrix of a Linear Transformation
pagenum: 70; label: 1.10
title: Linear Models in Business, Science, and Engineering
pagenum: 80; title: Supplementary Exercises
pagenum: 88; label: Chapter 2
title: Matrix Algebra
pagenum: 91; title: Introductory Example: Computer Models in Aircraft Design
pagenum: 91; label: 2.1
title: Matrix Operations
pagenum: 92; label: 2.2
title: The Inverse of a Matrix
pagenum: 102; label: 2.3
title: Characterizations of Invertible Matrices
pagenum: 111; label: 2.4
title: Partitioned Matrices
pagenum: 117; label: 2.5
title: Matrix Factorizations
pagenum: 123; label: 2.6
title: The Leontief Input-Output Model
pagenum: 132; label: 2.7
title: Applications to Computer Graphics
pagenum: 138; label: 2.8
title: Subspaces of \(\mathbb{R}^n\)
pagenum: 146; label: 2.9
title: Dimension and Rank
pagenum: 153; title: Supplementary Exercises
pagenum: 160; label: Chapter 3
title: Determinants
pagenum: 163; title: Introductory Example: Random Paths and Distortion
pagenum: 163; label: 3.1
title: Introduction to Determinants
pagenum: 164; label: 3.2
title: Properties of Determinants
pagenum: 169; label: 3.3
title: Cramer's Rule, Volume, and Linear Transformations
pagenum: 177; title: Supplementary Exercises
pagenum: 185; label: Chapter 4
title: Vector Spaces
pagenum: 189; title: Introductory Example: Space Flight and Control Systems
pagenum: 189; label: 4.1
title: Vector Spaces and Subspaces
pagenum: 190; label: 4.2
title: Null Spaces, Column Spaces, and Linear Transformations
pagenum: 198; label: 4.3
title: Linearly Independent Sets; Bases
pagenum: 208; label: 4.4
title: Coordinate Systems
pagenum: 216; label: 4.5
title: The Dimension of a Vector Space
pagenum: 225; label: 4.6
title: Rank
pagenum: 230; label: 4.7
title: Change of Basis
pagenum: 239; label: 4.8
title: Applications to Difference Equations
pagenum: 244; label: 4.9
title: Applications to Markov Chains
pagenum: 253; title: Supplementary Exercises
pagenum: 262; label: Chapter 5
title: Eigenvalues and Eigenvectors
pagenum: 265; title: Introductory Example: Dynamical Systems and Spotted Owls
pagenum: 265; label: 5.1
title: Eigenvectors and Eigenvalues
pagenum: 266; label: 5.2
title: The Characteristic Equation
pagenum: 273; label: 5.3
title: Diagonalization
pagenum: 281; label: 5.4
title: Eigenvectors and Linear Transformations
pagenum: 288; label: 5.5
title: Complex Eigenvalues
pagenum: 295; label: 5.6
title: Discrete Dynamical Systems
pagenum: 301; label: 5.7
title: Applications to Differential Equations
pagenum: 311; label: 5.8
title: Iterative Estimates for Eigenvalues
pagenum: 319; title: Supplementary Exercises
pagenum: 326; label: Chapter 6
title: Orthogonality and Least Squares
pagenum: 329; title: Introductory Example: The North American Datum and GPS Navigation
pagenum: 329; label: 6.1
title: Inner Product, Length, and Orthogonality
pagenum: 330; label: 6.2
title: Orthogonal Sets
pagenum: 338; label: 6.3
title: Orthogonal Projections
pagenum: 347; label: 6.4
title: The Gram-Schmidt Process
pagenum: 354; label: 6.5
title: Least-Squares Problems
pagenum: 360; label: 6.6
title: Applications to Linear Models
pagenum: 368; label: 6.7
title: Inner Product Spaces
pagenum: 376; label: 6.8
title: Applications of Inner Product Spaces
pagenum: 383; title: Supplementary Exercises
pagenum: 390; label: Chapter 7
title: Symmetric Matrices and Quadratic Forms
pagenum: 393; title: Introductory Example: Multichannel Image Processing
pagenum: 393; label: 7.1
title: Diagonalization of Symmetric Matrices
pagenum: 395; label: 7.2
title: Quadratic Forms
pagenum: 401; label: 7.3
title: Constrained Optimization
pagenum: 408; label: 7.4
title: The Singular Value Decomposition
pagenum: 414; label: 7.5
title: Applications to Image Processing and Statistics
pagenum: 424; title: Supplementary Exercises
pagenum: 432; title: Appendixes; label: A
title: Uniqueness of the Reduced Echelon Form
pagenum: A1; label: B
title: Complex Numbers
pagenum: A2; title: Glossary
pagenum: A7; title: Answers to Odd-Numbered Exercises
pagenum: A17; title: Index
pagenum: I1; title: Photo Credits
pagenum: P1