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