Linear Algebra A Geometric Approach

Linear Algebra: A Geometric Approach, Second Edition, presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make the transition to more abstract advanced courses. The text guides students on how to think about mathematical concepts and write rigorous mathematical arguments.

 Preface
Foreword to the Instructor
Foreword to the Student Chapter 1. Vectors and Matrices
1. Vectors
2. Dot Product
3. Hyperplanes in Rn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications Chapter 2.  Matrix Algebra
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose Chapter 3. Vector Spaces
1. Subspaces of  Rn2. The Four Fundamental Subspaces
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces Chapter 4. Projections and Linear Transformations
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 Chapter 5. Determinants
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area in R2 and Signed Volume in R2 Chapter 6. Eigenvalues and Eigenvectors
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. The Spectral Theorem Chapter 7. Further Topics
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations For Further Reading
Answers to Selected Exercises
List of Blue Boxes
Index