Lie groups | Transformation (function)

Infinitesimal transformation

In mathematics, an infinitesimal transformation is a limiting form of small transformation. For example one may talk about an infinitesimal rotation of a rigid body, in three-dimensional space. This is conventionally represented by a 3×3 skew-symmetric matrix A. It is not the matrix of an actual rotation in space; but for small real values of a parameter ε the transformation is a small rotation, up to quantities of order ε2. (Wikipedia).

Video thumbnail

Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example

Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example In this lecture we demonstrate how a transformation group generator can transform a function on the geometric space when the transformation is infinitesimal. For this we use Gilmores 2-parameter scale/shift exa

From playlist Lie Groups and Lie Algebras

Video thumbnail

Linear Transformations: Onto

Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

Video thumbnail

Symmetrization

In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of

From playlist Linear Transformations

Video thumbnail

Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example

Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example A finite transformation is simply a lot of infinitesimal transformations! A Lie group, we have already show is a connected topological space and we know that any finite transformation can be built from a large product

From playlist Lie Groups and Lie Algebras

Video thumbnail

[Lesson 16] QED Prerequisites Thomas Precession Calculation

In this lecture we calculate and decompose the infinitesimal Lorentz Transformation which contains the Thomas Precession formula. The work in this lesson, and the last, is sourced from Jackson's text "Classical Electrodynamics." Please consider supporting this channel on Patreon: https:/

From playlist QED- Prerequisite Topics

Video thumbnail

Noether’s Theorem in Classical Dynamics : Continuous Symmetries by N. Mukunda

DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (

From playlist The Legacy of Emmy Noether

Video thumbnail

23: Time change of vectors in rotating systems

Jacob Linder: 16.02.2012, Classical mechanics (TFY4345), v2012 NTNU A full textbook covering the material in the lectures in detail can be downloaded for free here: http://bookboon.com/en/introduction-to-lagrangian-hamiltonian-mechanics-ebook

From playlist NTNU: TFY 4345 - Classical Mechanics | CosmoLearning Physics

Video thumbnail

Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Philippe Nabonnand - 17/11/17

En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Élie Cartan suit le cours de géométrie de Gaston Darboux Philippe Nabonnand, Archives Henri Poincaré, Université de Lorraine) À l’occasion du centenaire de la mort de Gaston Darboux, l’Institut Henri Poincaré souhaite

From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017

Video thumbnail

[Lesson 15 and 2/3] QED Prerequisites Thomas Precession : The Set Up

In this lesson we set up a model that will allow us to discover the physics behind Thomas Precession. This is a very mysterious phenomenon due entirely to the fact that the world works via Minkowski/Lorentz geometry and not Euclidean/Galliean geometry. Thomas Precession is very subtle and

From playlist QED- Prerequisite Topics

Video thumbnail

What is General Relativity? Lesson 48: Ricci tensor and conformal transformations

What is General Relativity? Lesson 48: Ricci tensor and conformal transformations We introduce the Ricci tensor, curvature scalar, and begin the difficult derivation of the Weyl tensor. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussin

From playlist What is General Relativity?

Video thumbnail

2.2.2 What is a linear transformation?

2.2.2 What is a linear transformation?

From playlist LAFF - Week 2

Video thumbnail

Lecture 9 | Modern Physics: Classical Mechanics (Stanford)

Lecture 9 of Leonard Susskind's Modern Physics course concentrating on Classical Mechanics. Recorded December 20, 2007 at Stanford University. This Stanford Continuing Studies course is the first of a six-quarter sequence of classes exploring the essential theoretical foundations of mo

From playlist Course | Modern Physics: Classical Mechanics

Video thumbnail

Conformal Field Theory (CFT) | Infinitesimal Conformal Transformations

Conformal field theories are used in many areas of physics, from condensed matter physics, to statistical physics to string theory. They are defined as quantum field theories that are invariant under so-called conformal transformations. In this video, we will investigate these conformal tr

From playlist Particle Physics

Video thumbnail

Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators

Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P

From playlist Lie Groups and Lie Algebras

Video thumbnail

The Fourier Transform and Derivatives

This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow

From playlist Fourier

Related pages

Differential equation | Lie group | Symmetry | Mathematical analysis | Taylor's theorem | Theta operator | Operator (mathematics) | One-parameter group | Exponential function | Rotation | Rigid body | Limit (mathematics) | Connected space | Mathematics | Baker–Campbell–Hausdorff formula | Group theory | Lie algebra | Cross product | Hermann Weyl | Analytic function | Skew-symmetric matrix | Geometry | Jacobi identity