Lectures related to Context and applications: Simple applications

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Pseudorandomness: Theory and Applications

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Convex Optimization: Linear Algebra Review

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Canonical Correlation Analysis: Overview

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Eigenvalues and Eigenvectors Decomposition

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

Spectral Decomposition and SVD

Explores spectral decomposition of symmetric matrices and Singular Value Decomposition (SVD) for matrix decomposition.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Spectral Decomposition

Explores spectral and singular value decompositions of matrices.

Convex Optimization: Notation and Matrix Norms

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Singular Value Decomposition

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Retractions vector fields and tangent bundles: Tangent bundles

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Singular Value Decomposition: Example

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Singular Values: Definitions and Properties

Covers the concept of singular values in linear algebra and their properties, including diagonalization and practical examples.

Optimization on Manifolds

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its applications in practice.