Lectures related to Cholesky Factorization: Theory and Algorithm

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

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

Direct Methods for Linear Systems of Equations

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

Singular Value Decomposition: Applications and Interpretation

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

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

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.

Linear Algebra Review

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

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions for solving linear systems and simulating dynamics.

Matrix Decomposition: Triangular and Spectral

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

LU Decomposition Algorithm

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

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Matrix Inversion

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.

Eigenvalues and Eigenvectors Decomposition

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

QR Factorization: Least Squares System Resolution

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

Linear Algebra Review: Convex Optimization

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

LU Decomposition: Linear Systems Applications

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

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: Image Compression and Applications

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

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Construction of an Iterative Method

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