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Lecture 01: The Geometry of Linear Equations
Lecture 02: Elimination with Matrices
Lecture 03: Multiplication and Inverse Matrices
Lecture 06: Column Space and Nullspace
Lecture 05: Transposes, Permutations, Spaces R^n
Lecture 04: Factorization into A = LU
Lecture 09: Independence, Basis, and Dimension
Lecture 07: Solving Ax = 0: Pivot Variables, Special Solutions
Lecture 10: The Four Fundamental Subspaces
Lecture 08: Solving Ax = b: Row Reduced Form R
Lecture 21: Eigenvalues and Eigenvectors
Lecture 22: Diagonalization and Powers of A
Lecture 14: Orthogonal Vectors and Subspaces
Lecture 11: Matrix Spaces; Rank 1; Small World Graphs
Lecture 15: Projections onto Subspaces
Lecture 12: Graphs, Networks, Incidence Matrices
Lecture 18: Properties of Determinants
Lecture 17: Orthogonal Matrices and Gram-Schmidt
Lecture 13: Quiz 1 Review
Lecture 16: Projection Matrices and Least Squares
Lecture 19: Determinant Formulas and Cofactors
Lecture 23: Differential Equations and exp(At)
Lecture 20: Cramer's Rule, Inverse Matrix, and Volume
Lecture 01: Difference Methods for Ordinary Differential Equations
Lecture 25: Symmetric Matrices and Positive Definiteness
Lecture 28: Similar Matrices and Jordan Form
Lecture 29: Singular Value Decomposition
Lecture 30: Linear Transformations and Their Matrices
Lecture 31: Change of Basis; Image Compression
Linear Algebra vs Calculus
Lecture 24B: Quiz 2 Review
Gil Strang's Introduction to Highlights of Calculus
Lecture 24: Markov Matrices; Fourier Series
Lecture 27: Positive Definite Matrices and Minima
Lecture 26: Complex Matrices; Fast Fourier Transform
Lecture 33: Left and Right Inverses; Pseudoinverse
Lecture 34: Final Course Review
Big Picture of Calculus
Lecture 01: Positive Definite Matrices K = A'CA
Lecture 32: Quiz 3 Review
Big Picture: Derivatives
Lecture 02: Finite Differences, Accuracy, Stability, Convergence
Lecture 14: Financial Mathematics / Black-Scholes Equation
The Exponential Function
Big Picture: Integrals
Max and Min and Second Derivative
Lecture 23: Calculus of Variations / Weak Form
Lecture 03: The One-way Wave Equation and CFL / von Neumann Stability
Lecture 15: Iterative Methods and Preconditioners
Lecture 28: Linear Programming and Duality
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