Lectures related to Decomposition LLT: Example

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

Linear Algebra: Change of Basis Matrices

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Orthogonal Matrices and Eigenvalues

Explores orthogonal matrices, eigenvalues, and orientation-preserving transformations in linear algebra.

Linear Algebra: Operations and Applications

Explores operations and applications of linear algebra in solving equations and transformations.

Linear Algebra Review

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

Eigenspaces: Definitions and Examples MOOC: Linear Algebra (Part 2)

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Vector Spaces: Structure and Bases

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

Question of Motivation MOOC: Linear Algebra (Part 3)

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Linear systems resolution

Covers the resolution of linear systems and its link to optimization problems.

LU Decomposition Algorithm MOOC: Linear Algebra (Part 1)

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

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Linear Algebra: Matrix Representation

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

Linear Algebra: Systems of Equations and Transformations

Explores systems of linear equations, transformations, dilatation, rotation, and cross ratios in linear algebra.

Orthogonal Projections and Reflections

Covers the analytical expression of orthogonal projections and reflections in 2D space.

Linear Applications Overview

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

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Rotations (2D): Definitions and Analytical Expressions

Covers the concept of 2D rotations and their analytical expressions.

Singular Value Decomposition

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

Linear Algebra: CMS

Covers functions, compositions, and applications in linear algebra.

Integration of Rational Functions MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the integration of rational functions, decomposition into irreducible factors, and step-by-step integration examples.