Linear Algebra

Table of Contents

1. Cover
2. Title page
3. Contents
4. A list of Symbols
5. Preface
6. A Note to Students
7. Chapter 1. Matrices
   1. 1.1 Introduction
   2. 1.2 Basic Concepts
   3. 1.3 Matrix Operations and Their Properties
   4. 1.4 Invertible Matrices
   5. 1.5 Transpose of a Matrix
   6. 1.6 Partition of Matrices; Block Multiplication
8. Chapter 2. Systems of Linear Equations
   1. 2.1 Introduction
   2. 2.2 Gaussian Elimination
   3. 2.3 Elementary Row Operations
   4. 2.4 Row Reduction
   5. 2.5 Invertible Matrices Again
   6. 2.6 Determinant
9. Chapter 3. Vector Spaces
   1. 3.1 Introduction
   2. 3.2 Basic Concepts
   3. 3.3 Linear Independence
   4. 3.4 Basis and Dimension
   5. 3.5 Subspaces Again
   6. 3.6 Rank of a Matrix
   7. 3.7 Bases of Subspaces
   8. 3.8 Quotient Space
10. Chapter 4. Linear Maps and Matrices
    1. 4.1 Introduction
    2. 4.2 Basic Concepts
    3. 4.3 Isomorphism
    4. 4.4 Algebra of Linear Maps
    5. 4.5 Matrices of Linear Maps
11. Chapter 5. Linear Operators
    1. 5.1 Introduction
    2. 5.2 Polynomials Over Fields
    3. 5.3 Characteristic Polynomial and Eigenvalues
    4. 5.4 Minimal Polynomial
    5. 5.5 Invariant Subspaces
    6. 5.6 Some Basic Results
12. Chapter 6. Canonical Forms
    1. 6.1 Introduction
    2. 6.2 Primary Decomposition Theorem
    3. 6.3 Jordan Forms
    4. 6.4 Rational Canonical Form
13. Chapter 7. Bilinear Forms
    1. 7.1 Introduction
    2. 7.2 Basic Concepts
    3. 7.3 Bilinear Forms and Linear Functionals
    4. 7.4 Symmetric Bilinear Forms
    5. 7.5 Quadratic Forms
14. Chapter 8. Inner Product Spaces
    1. 8.1 Introduction
    2. 8.2 Hermitian Forms
    3. 8.3 Inner Product Space
    4. 8.4 Gram-Schmidt Orthogonalization Process
    5. 8.5 Adjoints
    6. 8.6 Unitary and Orthogonal Operators
    7. 8.7 Normal Operators
15. Chapter 9. Selected Topics
    1. 9.1 Introduction
    2. 9.2 Isometries
    3. 9.3 Real Quadratic Forms
    4. 9.4 Singular Value Decomposition
16. References
17. Copyright