In the theory of Lie groups, the exponential map is a map from the Lie algebra of a Lie group to the group, which allows one to recapture the local group structure from the Lie algebra. The existence of the exponential map is one of the primary reasons that Lie algebras are a useful tool for studying Lie groups. The ordinary exponential function of mathematical analysis is a special case of the exponential map when is the multiplicative group of positive real numbers (whose Lie algebra is the additive group of all real numbers). The exponential map of a Lie group satisfies many properties analogous to those of the ordinary exponential function, however, it also differs in many important respects. (Wikipedia).
This lecture is part of an online graduate course on Lie groups. We define the exponential map for matrix groups and describe its basic properties. (We also sketch two ways to define it for general Lie groups.) We give an example to show that it need not be surjective even for connected g
From playlist Lie groups
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Introduces notation and formulas for exponential growth models, with solutions to guided problems.
From playlist Discrete Math
Applying Exponential Models // Math Minute [#34] [ALGEBRA]
Exponential functions work a lot like linear functions. There are typically two parameters that guide the use of the exponential function: the initial value (like the y-intercept of a linear function) and the factor of growth (like the slope of a linear function). There are some additional
From playlist Math Minutes
PreCalculus - Exponential Function (9 of 13) Slope of an Exponential Function
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how the slope of an exponential function is the exponential function. Next video in the Exponential Function can be seen at: http://youtu.be/LDmyh-Dxngs
From playlist Michel van Biezen: PRECALCULUS 1-5 - ALGEBRA REVIEW
Algebra Ch 46: Exponential Function (1 of 12) What is an Exponential Function?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn an exponential function is a function in the form of f(x)=b^x where b=base (b(greater than)0, and b does not=1) and x=e
From playlist THE "WHAT IS" PLAYLIST
Derivatives: Exponential Functions
This is the fourth video of a series from the Worldwide Center of Mathematics explaining the basic rules for calculating derivatives. This video deals with derivatives of exponential functions. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Rules for Calculating Derivatives
Introduction to geometric invariant theory 1: Noncommutative duality - Ankit Garg
Optimization, Complexity and Invariant Theory Topic: Introduction to geometric invariant theory 1: Noncommutative duality Speaker: Ankit Garg Affiliation: Microsoft Research New England Date: June 5. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Lie Group Integrators for Animation and Control of Vehicles - Talk (4/4)
This video is a conference presentation of the paper "Lie Group Integrators for Animation and Control of Vehicles" given by Keenan Crane in August 2009 -- see http://keenan.is/nonholonomic for more information Lie Group Integrators for Animation and Control of Vehicles Marin Kobilarov, Ke
From playlist Lie Group Integrators Talk
The Green - Tao Theorem (Lecture 1) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group
Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state
From playlist Lie Groups and Lie Algebras
The orbit method for (certain) pro-p groups (Lecture 2) by Uri Onn
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3)
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3) In this video lesson we construct the Lie group elements of SO(3) starting from the defining property of SO(3) and the Lie algebra of so(3). To do this we review the Caley-Hamilton theorem that a square matrix satisfies its own cha
From playlist Lie Groups and Lie Algebras
Expected Value of the Exponential Distribution | Exponential Random Variables, Probability Theory
What is the expected value of the exponential distribution and how do we find it? In today's video we will prove the expected value of the exponential distribution using the probability density function and the definition of the expected value for a continuous random variable. It's gonna b
From playlist Probability Theory
Richard Thomas - The Katz-Klemm-Vafa formula
Richard THOMAS (Imperial College London, UK)
From playlist Algèbre, Géométrie et Physique : une conférence en l'honneur
Lie Groups and Lie Algebras: Lesson 26: Review!
Lie Groups and Lie Algebras: Lesson 26: Review! It never hurts to recap! https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Friedrich Wagemann: Deformation quantization of Leibniz algebras
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Is the variety of singular tuples of matrices a null cone? - Viswambhara Makam
Computer Science/Discrete Mathematics Seminar II Topic: Is the variety of singular tuples of matrices a null cone? - Speaker: Viswambhara Makam Affiliation: Member, School of Mathematics Date: February 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
In this video, I define the exponential derivative of a function using power series, and then show something really neat: For “most” functions (those that have a power series expansion), the exponential derivative is just shifting the function by 1! I also derive the product rule for exp
From playlist Calculus