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Table of Contents
Foreword to the Instructor
Foreword to the Student
2. Dot Product
3. Hyperplanes in Rn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose
1. Subspaces of Rn
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces
1. Inconsistent Systems and Projection
2. Orthogonal Bases
3. The Matrix of a Linear Transformation and the Change-of-Basis Formula
4. Linear Transformations on Abstract Vector Spaces
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area in R2 and Signed Volume in R2
1. The Characteristic Polynomial
4. The Spectral Theorem
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations
Answers to Selected Exercises
List of Blue Boxes