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Lecture
Latent Factor Analysis: Movie Genre Classification
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Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition
Explores matrix decompositions for solving linear systems and simulating dynamics.
Spectral Decomposition and SVD
Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.
Singular Value Decomposition: Example
Explains the step-by-step process of finding the singular value decomposition of a matrix.
Singular Value Decomposition: Image Compression and Applications
Covers Singular Value Decomposition, focusing on its application in image compression and data representation.
Construction of an Iterative Method
Covers the construction of an iterative method for linear systems by decomposing a matrix A into P, T, and P_A.
Jordan Normal Form: Theory and Applications
Explores the Jordan normal form and its applications in linear algebra, focusing on diagonalization and cyclic bases.
Singular Value Decomposition: Applications and Interpretation
Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.
Orthogonal Projections and Reflections
Covers the analytical expression of orthogonal projections and reflections in 2D space.
Spectral Clustering: Theory and Applications
Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.
Matrix Decomposition: Triangular and Spectral
Covers the decomposition of matrices into triangular blocks and spectral decomposition.