CHAPTER I
Vectors
1. Definition of Poinls in Space
2. Located Vectors
3. Scalar Product
4. The Norm of a Vector
5. Parametric Lines
6. Planes
CHAPTER II
Matrices and LiNear Equations
1. Matrices
2. Multiplication of Matrices
3. Homogeneous Linear Equations and Elimination
4. Row Operations and Gauss Elimination
5 Row Operations and Elementary Matrices
6. Linear Combinations
CHAPTER III
Vector Spaces
1. Definitions
2. Linear Combinations
3. Convex Sets
. Linear Independence
5. Dimension
6. The Rank cf a Matrix
CHAPTER IV
Linear Mappings
1. Mappings
2. Linear Mappings.
3. The Kernel and Image of a Linear Map
4. The Rank and Linear Equations Again
5. The Matrix Associated with a Linear Map
Appendix: Change of Bases
CHAPTER V
Composition and Inverse Mappings
1. Composition of Linear Maps
2. Inverses
CHAPTER VI
Scalar Products and Orthogonality
1. Scalar Products
2. Orthogonal Bases
3. Bilinear Maps and Matrices
CHAPTER VII
Determinants
1. Determinants of Order 2
2. 3 x 3 and n x n Determinants
3. The Rank of a Matrix and Subdeterminants
4. Cramer's Rule
5. Inverse of a Matrix
6. Determinants as Area and Volume
CHAPTER VIII
Eigenveetors and Eigenvalues
1. Eigenvectors and Eigenvalues
2. The Characteristic Polynomial
3. Eigenvalues and Eigenvectors of Symmetric Matrices
4. Diagonalization of a Symmetric Linear Map
Appendix. Complex Numbers
Answers to Exercises
Index
