Lectures related to Signal Representations

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

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.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

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

Linear Algebra Review: Convex Optimization

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

Singular Value Decomposition: Applications and Interpretation

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

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Singular Value Decomposition (SVD)

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

Matrix Calculus: Rank and Decomposition

Covers matrix rank, determinant, and decomposition in linear algebra.

Vector Spaces: Structure and Bases

Covers vector spaces, bases, and decomposition of vectors in R³.

Functional Analysis I: Norms and Bounded Operators

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

SVD: Singular Value Decomposition

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

Convex Optimization: Notation and Matrix Norms

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

Singular Value Decomposition: Image Compression and Applications

Covers Singular Value Decomposition, focusing on its application in image compression and data representation.

Singular Value Decomposition

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

Singular Value Decomposition

Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.