A First Course in Linear Algebra [black&white only]

Key definitions, theorems and formulas (part 1 of 2)
TItle
Preface
Contents
To the Student
1. Systems of Linear Equations and Matrices
1.1. Systems of Linear Equations: Matrix Methods
1.2. Linear Systems without Unique Solutions
1.3. Matrix Arithmetic
1.4. Matrix Algebra
1.5. Matrix Inversion
1.6. Partitioned Matrices: Numerical Considerations
1.7. Extended Application: Networks and Graphs
Chapter 1 Summary
2. Determinants
2.1. The Determinant Function and Cramer's Rule
2.2. Laplace Expansion of Determinants
2.3. Properties of Determinants
2.4. Determinants and Matrix Inversion
Chapter 2 Summary
3. Vector Spaces
3.1. Examples and Definition of a Vector Space
3.2. Linear Dependence and Independence
3.3. Spanning Set: Subspace
3.4. Ordered Basis and Dimension
3.5. Matrices: Row and Column Spaces
Chapter 3 Summary
4. Inner Product Spaces
4.1. Distance and Angle in R^2 and R^3
4.2. Cross Products in R^3 (optional)
4.3. Real Inner Products
4.4. Geometry in Real Inner-Product Spaces
4.5. The Gram-Schmidt Process
4.6. Complex Vectors, Matrices, Inner Products
4.7. Extended Application: Least Squares Fit
Chapter 4 Summary
5. Linear Transformations
5.1. Definitions and Examples
5.2. The Range and Kernel of a Linear Transformation
5.3. Matrix Representations
5.4. The Algebra of Linear Transformations
5.5. Change of Basis and Similarity
5.6. Orthogonal Linear Transformations
Chapter 5 Summary
6. Eigenvalues, Eigenvectors, and Some Applications
6.1. Eigenvalues and Eigenvectors
6.2. Similarity to a Diagonal Matrix
6.3. Real Symmetric Matrices
6.4. Quadratic Forms, Conics, and Quadric Surfaces
6.5. Extended Application: Markov Chains
6.6. Complex Eigenvalues
6.7. Extended Application: Systems of Differential Equations
Chapter 6 Summary
Appendices
A.1. The Complex Numbers
A.2. Sets and Functions
A.3. Algorithms
A.4. References
A.5. The Greek Alphabet and Frequently Used Symbols
Answers and Solutions to Selected Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Index
Key definitions, theorems and formulas (part 2 of 2)