Linear Algebra

• Linear Algebra Course Glossary (From Instructor)

• Lecture 1: Basics of Linear Systems
• Lecture 2: Solving Systems and RREF
• Lecture 3: Matrices and Gauss-Jordan Elimination
• Lecture 4: Augmented Matrices and Linear Combinations
• Lecture 5: Matrix Multiplication and Matrices as Functions
• Lecture 6: Matrix Transformations, Page Rank, Fibonacci
• Lecture 7: Linear Transformations
• Lecture 8: Orthogonal Projections
• Lecture 9: Orthogonal Projection and Reflections
• Lecture 10: Composition and Matrix Multiplication
• Lecture 11: Composition and Matrix Multiplication Continued
• Lecture 12: Invertible Matrices
• Lecture 13: Invertible Matrices Continued
• Lecture 14: Span, Kernel, and Image
• Lecture 15: Linear Independance
• Lecture 16: Subspaces and Bases
• Lecture 17: Bases Continued
• Lecture 18: Proof of Fundamental Theorem of Linear Algebra
• Lecture 19: Dimensions of Subspaces, Rank, and Nullity
• Lecture 20: Coordinates Relative to a Basis
• Lecture 21: Coordinates and Linear Transformations
• Lecture 22: Orthogonality and Subspaces
• Lecture 23: Orthogonal Decomposition Theorem and Graham Schmitt,
• Lecture 24: Matrix Transposes
• Lecture 25: Least Squares Solutions
• Lecture 26: Least Squares Solutions Continued
• Lecture 27: Determinants
• Lecture 28: Determinants Continued
• Lecture 29: Co-factor Expansion
• Lecture 30: Determinants and Volume
• Lecture 31: Diagonalization
• Lecture 32: Eigenvectors and Eigenvalues
• Lecture 33: Eigenvectors and Eigenvalues Continued
• Lecture 34: Eigenvectors and Eigenvalues Continued
• Lecture 35: Transition Matrices and Distribution Vectors
• Lecture 36: Complex Eigenvectors and Eigenvalues
• Lecture 37: Spectral Theorem and Singular Value Decomposition Theorem
• Lecture 38: Vector Spaces
• Lecture 39: Linear Approximation on Non-Linear Functions