Lectures related to Geometric algebra

Geometric Transformations: Reflections and Translations

Explores reflections and translations in geometric transformations, demonstrating their stability and practical applications.

Geometry II: Modern Geometric Transformations

Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.

Vectors in Space: Properties and Interpretations

Explores properties and interpretations of vectors in space, including mixed product and linear dependence.

Why are there so many saddle points?: Loss landscape and optimization methods

Explores the reasons behind the abundance of saddle points in deep learning optimization, emphasizing statistical and geometric arguments.

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Introduction de la ROTORÉFLEXION

Introduces rotoréflexion, a transformation involving reflections and rotations, with practical geometric applications.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Geometric Examples

Explores geometric examples related to linear applications in algebra.

Geometric Rotations in 2D

Covers the geometric definition of rotations in 2D and analytical expressions for rotations using matrices.

Translations and Homotheties

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

Geometric Properties of Dot Product

Covers the geometric properties of the dot product and its algebraic aspects.

Scalar Product: Geometric Properties

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Rotations (2D): Definitions and Analytical Expressions

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

AI4Science at Microsoft: Catalyst Design & Material Discovery

Explores AI4Science at Microsoft, focusing on catalyst design, reaction mechanisms, and material discovery using Clifford algebra.

Geometric Interpretation of Determinants

Explores the geometric interpretation of determinants in R2 and R3 vector spaces.

Translations and Homotheties

Covers translations, homotheties, and their geometric properties, including reversibility and composition.

Isometries: Final Panorama

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.

Hyperstatic Structures and Principle of Virtual Work

Covers hyperstatic structures, pre-stressed structures, and limitations of geometric linearity.

Vector Spaces: Definition, R2

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.