Linear Algebra and Its Applications with R (Textbooks in Mathematics) [1 ed.] 0367486849, 9780367486846

Table of contents :
Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
1. Systems of Linear Equations and Matrices
1.1. Introductory Example from Statistics
1.2. What Is a Matrix? What Is a Vector?
1.2.1. Task Completion Checklist
1.2.2. Working Examples
1.2.3. Matrix and Vector
1.2.4. Checkmarks
1.2.5. Conceptual Quizzes
1.2.6. Regular Exercises
1.2.7. Lab Exercises
1.2.8. Practical Applications
1.2.9. Supplements with python Code
1.3. Systems of Linear Equations
1.3.1. Task Completion Checklist
1.3.2. Working Examples
1.3.3. System of Linear Equations
1.3.4. Checkmarks
1.3.5. Conceptual Quizzes
1.3.6. Regular Exercises
1.3.7. Lab Exercises
1.3.8. Practical Applications
1.3.9. Supplements with python Code
1.4. Echelon Form
1.4.1. Task Completion Checklist
1.4.2. Working Examples
1.4.3. Echelon Form
1.4.4. Checkmarks
1.4.5. Conceptual Quizzes
1.4.6. Regular Exercises
1.4.7. Lab Exercises
1.4.8. Practical Applications
1.4.9. Supplements with python Code
1.5. Discussion
2. Matrix Arithmetic
2.1. Introductory Example from Statistics
2.2. Matrix Operations
2.2.1. Task Completion Checklist
2.2.2. Working Examples
2.2.3. Matrix Operations
2.2.4. Checkmarks
2.2.5. Conceptual Quizzes
2.2.6. Regular Exercises
2.2.7. Lab Exercises
2.2.8. Practical Applications
2.2.9. Supplements with python Code
2.3. Properties of Matrix Operations and Matrix Inverse
2.3.1. Task Completion Checklist
2.3.2. Working Examples
2.3.3. Properties of Matrix Operations and Matrix Inverse
2.3.4. Checkmarks
2.3.5. Conceptual Quizzes
2.3.6. Regular Exercises
2.3.7. Lab Exercises
2.3.8. Practical Applications
2.3.9. Supplements with python Code
2.4. Elementary Matrices
2.4.1. Task Completion Checklist
2.4.2. Working Examples
2.4.3. Elementary Matrices
2.4.4. Checkmarks
2.4.5. Conceptual Quizzes
2.4.6. Regular Exercises
2.4.7. Lab Exercises
2.4.8. Practical Applications
2.4.9. Supplements with python Code
2.5. Discussion
3. Determinants
3.1. Introductory Example from Astronomy
3.2. Determinants
3.2.1. Task Completion Checklist
3.2.2. Working Examples
3.3. Introduction of Determinants
3.3.1. Checkmarks
3.3.2. Conceptual Quizzes
3.3.3. Regular Exercises
3.3.4. Lab Exercises
3.3.5. Practical Applications
3.3.6. Supplements with python Code
3.4. Properties of Determinants
3.4.1. Task Completion Checklist
3.4.2. Working Examples
3.4.3. Properties of Determinants
3.4.4. Checkmarks
3.4.5. Conceptual Quizzes
3.4.6. Regular Quizzes
3.4.7. Lab Exercises
3.4.8. Practical Applications
3.4.9. Supplements with python Code
3.5. Cramer's Rule
3.5.1. Task Completion Checklist
3.5.2. Working Examples
3.5.3. Cramer's Rule
3.5.4. Checkmarks
3.5.5. Conceptual Quizzes
3.5.6. Regular Exercises
3.5.7. Lab Exercises
3.5.8. Practical Applications
3.5.9. Supplements with python Code
3.6. Discussion
4. Vector Spaces
4.1. Introductory Example from Data Science
4.2. Vector Spaces and Subspaces
4.2.1. Task Completion Checklist
4.2.2. Working Examples
4.2.3. Vector Spaces and Vector Subspaces
4.2.4. Checkmarks
4.2.5. Conceptual Quizzes
4.2.6. Regular Exercises
4.2.7. Lab Exercises
4.2.8. Practical Applications
4.2.9. Supplements with python Code
4.3. Null Space, Column Space, and Row Space
4.3.1. Task Completion Checklist
4.3.2. Working Examples
4.3.3. Null Space, Column Space, and Row Space
4.3.4. Checkmarks
4.3.5. Conceptual Quizzes
4.3.6. Regular Exercises
4.3.7. Lab Exercises
4.3.8. Practical Applications
4.3.9. Supplements with python Code
4.4. Spanning Sets and Bases
4.4.1. Task Completion Checklist
4.4.2. Working Examples
4.4.3. Spanning Sets and Bases
4.4.4. Checkmarks
4.4.5. Conceptual Quizzes
4.4.6. Regular Exercises
4.4.7. Lab Exercises
4.4.8. Practical Applications
4.4.9. Supplements with python Code
4.5. Coordinates Systems and Change of Basis
4.5.1. Task Completion Checklist
4.5.2. Working Examples
4.5.3. Coordinate Systems and Change of Basis
4.5.4. Checkmarks
4.5.5. Conceptual Quizzes
4.5.6. Regular Exercises
4.5.7. Lab Exercises
4.5.8. Practical Applications
4.5.9. Supplements with python Code
4.6. Discussion
5. Inner Product Space
5.1. Introductory Example from Statistics
5.2. Inner Products
5.2.1. Task Completion Checklist
5.2.2. Working Examples
5.2.3. Inner Products
5.2.4. Checkmarks
5.2.5. Conceptual Quizzes
5.2.6. Regular Exercises
5.2.7. Lab Exercises
5.2.8. Practical Applications
5.2.9. Supplements with python Code
5.3. Angles and Orthogonality
5.3.1. Task Completion Checklist
5.3.2. Working Examples
5.3.3. Angles and Orthogonality
5.3.4. Checkmarks
5.3.5. Conceptual Quizzes
5.3.6. Regular Exercises
5.3.7. Lab Exercises
5.3.8. Practical Applications
5.3.9. Supplements with python Code
5.4. Discussion
6. Eigen Values and Eigen Vectors
6.1. Introductory Example from Data Science: Image Compression
6.2. Eigen Values and Eigen Vectors
6.2.1. Task Completion Checklist
6.2.2. Working Examples
6.2.3. Eigen Values and Eigen Vectors
6.2.4. Checkmarks
6.2.5. Conceptual Quizzes
6.2.6. Regular Exercises
6.2.7. Lab Exercises
6.2.8. Practical Applications
6.2.9. Supplements with python Code
6.3. Diagonalization
6.3.1. Task Completion Checklist
6.3.2. Working Examples
6.3.3. Diagonalization
6.3.4. Checkmarks
6.3.5. Conceptual Quizzes
6.3.6. Regular Exercises
6.3.7. Lab Exercises
6.3.8. Practical Applications
6.3.9. Supplements with python Code
6.4. Discussion
7. Linear Regression
7.1. Introductory Example from Statistics
7.2. Simple Linear Regression
7.2.1. Task Completion Checklist
7.2.2. Basic Terminology
7.2.3. Simple Linear Regression
7.2.4. Multiple Linear Regression
7.2.5. Checkmarks
7.2.6. Practical Applications
7.2.7. Supplements with python Code
8. Linear Programming
8.1. Introductory Example from Optimization
8.2. Linear Programming
8.2.1. Task Completion Checklist
8.2.2. Basic Terminology
8.2.3. Linear Programming
8.2.4. Checkmarks
8.2.5. Practical Applications
8.2.6. Supplements with python Code
9. Network Analysis
9.1. Introductory Example from Network Analysis
9.2. Graphs and Networks
9.2.1. Task Completion Checklist
9.2.2. Basic Terminology
9.2.3. Properties of Laplacian Matrices
9.2.4. Checkmarks
9.2.5. Practical Applications
9.2.6. Supplements with python Code
9.3. Discussion
Appendices
A. Introduction to RStudio via Amazon Web Services (AWS)
A.1. Setting Up AWS
A.2. Basics in RStudio
B. Introduction to R
B.1. Display in R
B.2. Setting Up the R Programming Environment
B.3. Getting Started with Objects in R
B.3.1. Assigning an Object (Variable)
B.3.2. Boolean Operators
B.4. Saving a Session and Data
Bibliography
Index