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Unit I Overview
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1.1 The Geometry of Linear Equations
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1.2 An Overview of Key Ideas
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1.3 Elimination with Matrices
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1.4 Multiplication and Inverse Matrices
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1.5 Factorization into A = LU
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1.6 Transposes, Permutations, Vector Spaces
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1.7 Column Space and Nullspace
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1.8 Solving Ax = 0: Pivot Variables, Special Solutions
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1.9 Solving Ax = b: Row Reduced Form R
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2.0 Independence, Basis and Dimension
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2.1 The Four Fundamental Subspaces
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2.2 Matrix Spaces; Rank 1; Small World Graphs
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2.3 Graphs, Networks, Incidence Matrices
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2.4 Exam 1 Review
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2.5 Exam 1
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Unit II Overview
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2.1 Orthogonal Vectors and Subspaces
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2.2 Projections onto Subspaces
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2.3 Projection Matrices and Least Squares
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2.4 Orthogonal Matrices and Gram-Schmidt
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2.5 Properties of Determinants
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2.6 Determinant Formulas and Cofactors
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2.7 Cramer's Rule, Inverse Matrix and Volume
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2.8 Eigenvalues and Eigenvectors
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2.9 Diagonalization and Power of A
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3.0 Differential Equations and exp(At)
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3.1 Markov Matrices; Fourier Series
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3.2 Exam 2 Review
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3.3 Exam 2
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Unit III Overview
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3.1 Symmetric Matrices and Positive Definiteness
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3.2 Complex Matrices; Fast Fourier Transform (FFT)
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3.3 Positive Definite Matrices and Minima
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3.4 Similar Matrices and Jordan Form
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3.5 Singular Value Decomposition
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3.6 Linear Transformations and Their Matrices
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3.7 Change of Basis; Image Compression
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3.8 Left and Right Inverses; Pseudoinverse
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Exam 3 Review
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Exam 3
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