Introductory Linear Algebra

- Preface
- Notations and Conventions
- Chapter 1 Euclidean Spaces
- 1.1 Vectors
- 1.2 Lines in R2
- 1.3 Length and Dot Product
- 1.4 Orthogonal Projection
- 1.5 Area in R2 and 2×2 Determinants
- 1.6 Planes in R3
- Chapter 2 System of Linear Equations
- 2.1 Terminologies and Definitions
- 2.2 Gaussian Elimination
- Chapter 3 Matrix Algebra
- 3.1 Definitions and Properties of Matrix Operations
- 3.2 Linear Systems Revisited
- 3.3 Invertible Matrix
- 3.4 Square Matrices of Special Forms
- 3.5 Elementary Matrices
- Chapter 4 Determinants
- 4.1 Definition
- 4.2 Properties of Determinants
- 4.3 Adjoint Matrix and Cramer's Rule
- 4.4 Cross Product in R3
- Chapter 5 Subspaces of Rn and Their Bases
- 5.1 Subspaces of Rn
- 5.2 Linear Combination and Linear Independence
- 5.3 Basis and Dimension
- 5.4 Coordinates with Respect to Ordered Bases
- Chapter 6 Linear Transformations
- 6.1 Matrix Transformations
- 6.2 Linear Operators on R2 and R3
- Chapter 7 Eigenvalues, Eigenvectors and Diagonalization
- 7.1 Definitions and Properties of Eigenvalues and Eigenvectors
- 7.2 Diagonalizability
- 7.3 Diagonalization
- Answer Keys to Selected Exercise Problems
- Suggested Further Readings
- Index