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Introduction to Linear Algebra
Application: Data Compression
Systems of Linear Equations
1. What Is Linear Algebra?
2. Systems of Linear Equations
3. Row Reduction and Echelon Forms
4. Vectors in N Dimensions
5. Matrix Equations
Application: Polynomial Interpolation
Quiz 1
Linear Transformations and Matrix Operations
6. Linear Independence
7. Linear Transformations
8. The Matrix of a Linear Transformation
9. Matrix Operations
10. The Inverse of a Matrix
Application: Economic Models
Quiz 2
LU Factorization and Determinants
11. The LU Factorization
12. Determinants
13. Properties of Determinants
14. Applications of Determinants
Quiz 3
Eigenvalues and Inner Products
15. Eigenvectors and Eigenvalues
16. The Characteristic Equation
17. Diagonalization
18. Inner Products
19. Orthogonal Sets
Application: Quantum Entanglement
Quiz 4
Least Squares and Singular Value Decomposition
20. Orthogonal Projections
21. The Gram–Schmidt Process
22. Least-Squares Problems
23. Diagonalization of Symmetric Matrices
24. Quadratic Forms
25. The Singular Value Decomposition
Application: Data Compression
Quiz 5
Certification
Final Exam
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25. The Singular Value Decomposition
Quiz 5
