Lectures related to Projections and Symmetries

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

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

Explores the scalar product of vectors, including properties and calculation methods.

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers the geometry of the triangle, including inequalities, heights, and centers.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Covers the geometric description of orthogonal projections and reflections in 2D, focusing on transformations and their properties.

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Explores counterfactuals in SEMs and D-Separation in graphical models.

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Delves into singular value decomposition and its applications in linear algebra.