Select a LectureLecture 1 - The Geometry of Linear EquationsLecture 2 - Elimination with MatricesLecture 3 - Multiplication and Inverse MatricesLecture 4 - Factorization into A = LU Lecture 5 - Transposes, Permutations, Spaces RnLecture 6 - Column Space and NullspaceLecture 7 - Solving Ax = 0: Pivot Variables, Special SolutionsLecture 8 - Solving Ax = b: Row Reduced Form RLecture 9 - Independence, Basis, and DimensionLecture 10 - The Four Fundamental SubspacesLecture 11 - Matrix Spaces; Rank 1; Small World GraphsLecture 12 - Graphs, Networks, Incidence MatricesLecture 13 - Quiz 1 ReviewLecture 14 - Orthogonal Vectors and SubspacesLecture 15 - Projections onto SubspacesLecture 16 - Projection Matrices and Least SquaresLecture 17 - Orthogonal Matrices and Gram-SchmidtLecture 18 - Properties of DeterminantsLecture 19 - Determinant Formulas and CofactorsLecture 20 - Cramer's Rule, Inverse Matrix, and VolumeLecture 21 - Eigenvalues and EigenvectorsLecture 22 - Diagonalization and Powers of ALecture 23 - Differential Equations and exp(At)Lecture 24 - Markov Matrices; Fourier SeriesLecture 24b - Quiz 2 ReviewLecture 25 - Symmetric Matrices and Positive DefinitenessLecture 26 - Symmetric Matrices and Positive DefinitenessLecture 27 - Positive Definite Matrices and MinimaLecture 28 - Similar Matrices and Jordan FormLecture 29 - Singular Value DecompositionLecture 30 - Linear Transformations and Their MatricesLecture 31 - Change of Basis; Image CompressionLecture 32 - Quiz 3 ReviewLecture 33 - Left and Right Inverses; PseudoinverseLecture 34 - Final Course Review
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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