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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.
Table of Contents
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 Rn
2. 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