Objective: Get better at linear algebra for the sake of it.
✅ Ch 01. Introduction to Systems of Linear Equations
✅ Ch 02. The Matrix Representation of a Linear System
Ch 03. Row Echelon Forms
Ch 04. Vector Representation
Ch 05. The Matrix-Vector Form of a Linear System
Ch 06. Linear Dependence and Independence
Ch 07. Matrix Transformations
Ch 08. Matrix Operations
Ch 09. Introduction to Eigenvalues and Eigenvectors
Ch 10. The Inverse of a Matrix
Ch 11. The Invertible Matrix Theorem
Ch 12. The Structure of \(R^n\)
Ch 13. The Null Space and Column Space of a Matrix
Ch 14. Eigenspaces of a Matrix
Ch 15. Bases and Dimension
Ch 16. The Determinant
Ch 17. The Characteristic Equation
Ch 18. Diagonalization
Ch 19. Approximating Eigenvalues and Eigenvectors
Ch 20. Complex Eigenvalues
Ch 21. Properties of Determinants
Ch 22. Vector Spaces
Ch 23. Bases for Vector Spaces
Ch 24. The Dimension of a Vector Space
Ch 25. Coordinate Vectors and Coordinate Transformations
Ch 26. Change of Basis
Ch 27. The Dot Product in \(R^n\)
Ch 28. Orthogonal and Orthonormal Bases in \(R^n\)
Ch 29. Inner Products
Ch 30. The Gram-Schmidt Process
Ch 31. Orthogonal Diagonalization
Ch 32. Quadratic Forms and the Principal Axis Theorem
Ch 33. The Singular Value Decomposition
Ch 34. Approximations Using the Singular Value Decomposition
Ch 35. Linear Transformations
Ch 36. The Matrix of a Linear Transformation
Ch 37. Eigenvalues of Linear Transformations