Lectures related to General Transformations

Symmetries of Navier-Stokes Equations

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Vector Transformation and Tense

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Geometric Transformations Compositions

Covers the composition of geometric transformations in 2D, focusing on rotations and reflections to achieve specific results.

Rotations (2D): Definitions and Analytical Expressions

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

Geometric Transformations: Rotations

Covers the analytical expression of rotations in different coordinate systems.

Geometric Transformations in R2 and R3: Visualizations and Rotations

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Geometric Transformations in the Plane: Orientation

Covers the concept of orientation in the plane and transformations using matrices.

Isometries in Euclidean Spaces

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

Lie Algebra of Lorentz Group

Covers the Lie algebra of the Lorentz group, focusing on boosts, rotations, and transformations.

Isometries: Final Panorama

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

Rotations: Angular Momentum

Covers angular momentum in rotations, including preservation of angles and vector products.

Geometry: Reflections and Transformations

Explores geometry transformations, emphasizing isometries, point reflections, rotations, and translations to illustrate fundamental geometric principles.

Geometry: Transformations and Isometries

Explores transformations and isometries in geometry, preserving properties through translations, rotations, and reflections.

Rotations in Quantum Mechanics

Introduces rotations in quantum mechanics, covering the Rodriguez formula and active transformations.

Isometries in Space: Orientation & Reflections

Explores isometries in space, transformations preserving lengths and angles, including reflections, rotations, and translations.

Rotations: Isometries and Axes

Explores rotations as isometries composed of reflections with common axes and the flexibility in choosing rotation axes.

Base Change for Rotation: Example MOOC: Linear Algebra (Part 3)

Explores changing bases for rotations, orthogonal planes, and vector transformations under rotation.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.

3D Rotations and Quaternions

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.