Linear Algebra A Modern Introduction 4th Edition by David Poole ISBN 1285463247 9781285463247

1. VECTORS.

Introduction: The Racetrack Game.

The Geometry and Algebra of Vectors. 

Length and Angle: The Dot Product. Exploration: Vectors and Geometry.

Lines and Planes. Exploration: The Cross Product.

Writing Project: Origins of the Dot Product and the Cross Product. Applications.

2. SYSTEMS OF LINEAR EQUATIONS.

Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems.

Writing Project: A History of Gaussian Elimination. Explorations: Lies My Computer Told Me; Partial Pivoting; Counting Operations: An Introduction to the Analysis of Algorithms.

Spanning Sets and Linear Independence.

Applications.

Vignette: The Global Positioning System.

Iterative Methods for Solving Linear Systems.

3. MATRICES.

Introduction: Matrices in Action.

Matrix Operations. Matrix Algebra.

The Inverse of a Matrix.

The LU Factorization. Subspaces, Basis, Dimension, and Rank.

Introduction to Linear Transformations.

Vignette: Robotics. Applications.

4. EIGENVALUES AND EIGENVECTORS.

Introduction: A Dynamical System on Graphs.

Introduction to Eigenvalues and Eigenvectors.

Determinants.

Writing Project: Which Came First-the Matrix or the Determinant?

Vignette: Lewis Carroll’s Condensation Method. 

5. ORTHOGONALITY.

Introduction: Shadows on a Wall.

Orthogonality in Rn.

Orthogonal Complements and Orthogonal Projections.

The Gram-Schmidt Process and the QR Factorization.

Explorations: The Modified QR Factorization; 

6. VECTOR SPACES.

Introduction: Fibonacci in (Vector) Space.

Vector Spaces and Subspaces.

 Linear Independence, Basis, and Dimension.

 Writing Project: The Rise of Vector Spaces.

 Exploration: Magic Squares. Change of Basis. Linear Transformations.

 The Kernel and Range of a Linear Transformation.

The Matrix of a Linear Transformation. 

7. DISTANCE AND APPROXIMATION.

Introduction: Taxicab Geometry.

 Inner Product Spaces.

Explorations: Vectors and Matrices with Complex Entries;

 Geometric Inequalities and Optimization Problems.

Norms and Distance Functions. 

8. CODES.

(Online) Code Vectors. 

Vignette: The Codabar System.

Error-Correcting Codes.

Dual Codes. 

Linear Codes.

The Minimum Distance of a Code.