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

Description

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)