Lecture
#1: The Geometry of Linear Equations
Lecture
#2: Elimination with Matrices
Lecture
#3: Multiplication and Inverse Matrices
Lecture
#4: Factorization into A = LU
Lecture
#5: Transposes, Permutations, Spaces R^n
Lecture
#6: Column Space and Nullspace
Lecture
#7: Solving Ax = 0: Pivot Variables, Special Solutions
Lecture
#8: Solving Ax = b: Row Reduced Form R
Lecture
#9: Independence, Basis, and Dimension
Lecture
#10: The Four Fundamental Subspaces
Lecture
#11: Matrix Spaces; Rank 1; Small World Graphs
Lecture
#12: Graphs, Networks, Incidence Matrices
Lecture
#13: Quiz 1 Review
Lecture
#14: Orthogonal Vectors and Subspaces
Lecture
#15: Projections onto Subspaces
Lecture
#16: Projection Matrices and Least Squares
Lecture
#17: Orthogonal Matrices and Gram-Schmidt
Lecture
#18: Properties of Determinants
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Lecture
#19: Determinant Formulas and Cofactors
Lecture
#20: Cramer's Rule, Inverse Matrix, and Volume
Lecture
#21: Eigenvalues and Eigenvectors
Lecture
#22: Diagonalization and Powers of A
Lecture
#23: Differential Equations and exp(At)
Lecture
#24 : Markov Matrices; Fourier Series
Lecture
#24.5 : Quiz 2 Review
Lecture
#25 : Symmetric Matrices and Positive Definiteness
Lecture
#26 : Complex Matrices; Fast Fourier Transform
Lecture
#27 : Positive Definite Matrices and Minima
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
Lecture
#32: Quiz 3 Review
Lecture
#33: Left and Right Inverses; Pseudoinverse
Lecture
#34: Final Course Review
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