Lectures related to Decomposition LLT: Example

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

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

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

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

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

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

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

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

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

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

Covers the properties and calculations of matrix determinants, including special cases and examples.

Covers bases, transformations, and matrix decompositions in linear algebra.

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

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

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

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

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

Covers the integration of rational functions and the decomposition into irreducible factors.

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