Lectures related to Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions for solving linear systems and simulating dynamics.

QR Factorization

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Singular Value Decomposition

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

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

LU Decomposition Algorithm

Covers the LU decomposition algorithm, transforming a matrix into L and U.

Singular Value Decomposition: Example

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

Singular Value Decomposition

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

Linear Algebra Review

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

Singular Value Decomposition: Image Compression and Applications

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

Eigenvalues and Eigenvectors Decomposition

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

Construction of an Iterative Method

Covers the construction of an iterative method for linear systems, emphasizing matrix decomposition and convexity.

LU Decomposition: Linear Systems Applications

Covers the LU decomposition method applied to linear systems, presenting the system in two steps.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

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

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Linear Algebra: Orthogonal Projection and QR Factorization

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Singular Value Decomposition

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

Linear Systems: Direct Methods

Explores linear systems, direct methods, Gauss elimination, LU decomposition, and computational complexity.

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: Convex Optimization

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