# Linear Algebra: A Modern Introduction, Third Edition Linear Algebra: A Modern Introduction, Third ...

ISBN: 9780538735452 / 0538735457

### Chapter 1

Vectors

 1.1 The Geometry and Algebra of Vectors Exercises p.16 1.2 Length and Angle: The Dot Product Exercises p.29 1.3 Lines and Planes Exercises p.44 1.4 Applications Exercises p.57 Chapter Review p.61

### Chapter 2

Systems Of Linear Equations

 2.1 Introduction to Systems of Linear Equations Exercises p.69 2.2 Direct Methods for Solving Linear Systems Exercises p.85 2.3 Spanning Sets and Linear Independence Exercises p.103 2.4 Applications Exercises p.119 2.5 Iterative Methods for Solving Linear Systems Exercises p.138 Chapter Review p.140

### Chapter 3

Matrices

 3.1 Matrix Operations Exercises p.158 3.2 Matrix Algebra Exercises p.167 3.3 The Inverse of a Matrix Exercises p.184 3.4 The LU Factorization Exercises p.195 3.5 Subspaces, Basis, Dimension, and Rank Exercises p.215 3.6 Introduction to Linear Transformations Exercises p.229 3.7 Applications Exercises p.256 Chapter Review p.263

### Chapter 4

Eigenvalues And Eigenvectors

 4.1 Introduction to Eigenvalues and Eigenvectors Exercises p.271 4.2 Determinants Exercises p.292 4.3 Eigenvalues and Eigenvectors of n X n Matrices Exercises p.309 4.4 Similarity and Diagonalization Exercises p.320 4.5 Iterative Methods for Computing Eigenvalues Exercises p.334 4.6 Applications and the Perron-Frobenius Theorem Exercises p.370 Chapter Review p.376

### Chapter 5

Orthogonality

 5.1 Orthogonality in R^n Exercises p.387 5.2 Orthogonal Complements and Orthogonal Projections Exercises p.398 5.3 The Gram-Schmidt Process and the QR Factorization Exercises p.405 5.4 Orthogonal Diagonalization of Symmetric Matrices Exercises p.418 5.5 Applications Exercises p.440 Chapter Review p.443

### Chapter 6

Vector Spaces

 6.1 Vector Spaces and Subspaces Exercises p.459 6.2 Linear Independence, Basis, and Dimension Exercises p.474 6.3 Change of Basis Exercises p.489 6.4 Linear Transformations Exercises p.498 6.5 The Kernel and Range of a Linear Transformation Exercises p.513 6.6 The Matrix of a Linear Transformation Exercises p.530 6.7 Applications Exercises p.547 Chapter Review p.550

### Chapter 7

Distance And Approximation

 7.1 Inner Product Spaces Exercises p.563 7.2 Norms and Distance Functions Exercises p.589 7.3 Least Squares Approximation Exercises p.609 7.4 The Singular Value Decomposition Exercises p.632 7.5 Applications Exercises p.644 Chapter Review p.646
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