Lectures related to Singular Values and Norms: Understanding Linear Maps with SVD

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.

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Linear Algebra Review: Convex Optimization

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

Signal Representations

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Linear Algebra: Singular Value Decomposition

Delves into singular value decomposition and its applications in linear algebra.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

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

Singular Value Decomposition (SVD)

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

Singular Value Decomposition: Applications and Interpretation

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

Singular Value Decomposition: Fundamentals and Applications

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Singular Value Decomposition

Introduces Singular Value Decomposition (SVD) in linear algebra, covering matrix factorization and properties with practical examples.

Matrix Representations: Linear Maps

Explores matrix representations of linear maps and their invariance, using examples and special cases.

Orthogonal Projection: Vector Decomposition

Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

Linear Algebra Basics

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Linear Maps and Matrices

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Linear Applications Overview

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.