Singular Value Decomposition: Theory and Applications

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Related lectures (46)

Eigenvalues and Eigenvectors Decomposition Log in to Mediaspace to watch this video

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Linear Algebra Review: Convex Optimization Log in to Mediaspace to watch this video

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

Linear Algebra: Bases and Transformations Log in to Mediaspace to watch this video

Covers bases, transformations, and matrix decompositions in linear algebra.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization Log in to Mediaspace to watch this video

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Latent Semantic Indexing: Concepts and Applications Log in to Mediaspace to watch this video

Explores Latent Semantic Indexing, a technique for mapping documents into a concept space for retrieval and classification.

Diagonalization of Symmetric Matrices Log in to Mediaspace to watch this video

Explores the diagonalization of symmetric matrices and the importance of Singular Value Decomposition.

Determinant, Area, and Volume Log in to Mediaspace to watch this video

Explores area determination, linear applications, matrix operations, and vector spaces.

Eigenstate Thermalization Hypothesis Log in to Mediaspace to watch this video

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Matrix Factorization: Optimization and Evaluation Log in to Mediaspace to watch this video

Explores matrix factorization optimization, evaluation methods, and challenges in recommendation systems.

Least Squares Solutions Log in to Mediaspace to watch this video

Covers least squares solutions for linear systems using matrix operations and normal systems, illustrated with examples.

Matrix Factorization: LU Decomposition Log in to Mediaspace to watch this video

Covers the LU decomposition method for matrix factorization and its application in electrical engineering.

Matrix Operations: Partitions and Blocks Log in to Mediaspace to watch this video

Covers matrix operations, including partitioning and block multiplication.

Low Rank Approximations Log in to Mediaspace to watch this video

Explores low rank approximations, spectral theorems, and orthogonality in matrices.

Tucker Decomposition: Multilinear rank and applications in data compression Log in to Mediaspace to watch this video

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Matrix Inversion: Basics and Properties Log in to Mediaspace to watch this video

Covers the basics of matrix inversion, properties of matrix multiplication, and the uniqueness of matrix inverses.

Matrix Factorization: LU Decomposition Log in to Mediaspace to watch this video

Explores LU decomposition for solving linear systems, focusing on determinants and cofactors.

Exponential of a Matrix Log in to Mediaspace to watch this video

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.

Matrix Multiplication: Applications and Properties Log in to Mediaspace to watch this video

Covers matrix multiplication, properties, and inverses in linear algebra.

Complex Numbers: Notations and Operations Log in to Mediaspace to watch this video

Covers notations, operations, isomorphism, and polar decomposition of complex numbers.

Orthogonal Projection: Theory and Applications Log in to Mediaspace to watch this video

Covers the theory of orthogonal projection in vector spaces and its practical applications.

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