Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
Dual spaces and linear functionals In this video, I introduce the concept of a dual space, which is the analog of a "shadow world" version, but for vector spaces. I also give some examples of linear and non-linear functionals. This seems like an innocent topic, but it has a huge number of
From playlist Dual Spaces
Functional Analysis Lecture 04 2014 01 30 Dual L^p spaces
Isometry between Dual L^p and L^p’; key lemma
From playlist Course 9: Basic Functional and Harmonic Analysis
Dual-Clutch Transmission / Double-Clutch Gearbox (Animation)
http://www.bring-knowledge-to-the-world.com/ Do you want to know how dual-clutch transmissions work? Then, this is the right video for you! Dual-clutch transmissions, which are also known as twin-clutch gearboxes or double-clutch transmissions, are automatic transmissions. The complexity b
From playlist Automotive Engineering
Hao Xu (7/26/22): Frobenius algebra structure of statistical manifold
Abstract: In information geometry, a statistical manifold is a Riemannian manifold (M,g) equipped with a totally symmetric (0,3)-tensor. We show that the tangent bundle of a statistical manifold has a Frobenius algebra structure if and only if the sectional K-curvature vanishes. This gives
From playlist Applied Geometry for Data Sciences 2022
In this video, I present a very classical example of a duality argument: Namely, I show that T^T is one-to-one if and only if T is onto and use that to show that T is one-to-one if and only if T^T is onto. This illustrates the beautiful interplay between a vector space and its dual space,
From playlist Dual Spaces
The "tangent plane" of the graph of a function is, well, a two-dimensional plane that is tangent to this graph. Here you can see what that looks like.
From playlist Multivariable calculus
On two geometric realizations of the anti-spherical module - Tsao-Hsien Chen
Geometric and Modular Representation Theory Seminar Topic: On two geometric realizations of the anti-spherical module Speaker: Tsao-Hsien Chen Affiliation: University of Minnesota, Twin Cities; Member, School of Mathematics Date: March 03, 2021 For more video please visit http://video.ia
From playlist Seminar on Geometric and Modular Representation Theory
Paul Nelson (Zurich): The orbit method, microlocal analysis and applications to L-functions
I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems concerning automorphic forms. The local applications include asymptotic expansions of relative ch
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
Shannon 100 - 28/10/2016 - Frank NIELSEN
The dual geometry of Shannon information and its applications Frank Nielsen (École Polytechnique) In information geometry, the negative Shannon entropy, called the Shannon information, is a strictly convex and differentiable function that induces a dually flat manifold structure equippe
From playlist Shannon 100
Panorama of Mathematics: Andrew Neitzke
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Andrew Neitzke: "Some new g
From playlist Panorama of Mathematics
Quantization By Branes And Geometric Langlands Lecture 2 by Edward Witten
PROGRAM : QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS : Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Quantization of Vortices (Lecture 1) by Nuno Romão
PROGRAM VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual field the
From playlist Vortex Moduli - 2023
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Thorben Kastenholz: Simplicial Volume of Total Spaces of Fiber Bundles
Thorben Kastenholz, University of Goettingen Title: Simplicial Volume of Total Spaces of Fiber Bundles It is a classical result that manifolds that are total spaces of fiber bundles, whose fiber has amenable fundamental group, have vanishing simplicial volume. In this talk I will explore t
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Ultimate Custom Car Time Capsule | Kip Cyprus Garage Tour
#classiccars #garagetours #leadsleds Travel back into the Fifties as we take a tour of Kip Cyprus’s garage full of early 50s and lead sled custom cars! Kip showcases three of his favorite customs. His 1950 Pontiac Chieftain comes with the original straight-eight 108 hp motor and sits ex
From playlist Ultimate Collection Tours | World's Rarest Cars
Dirac Delta Definition In this video, I define the Dirac Delta functional, and show that it is strictly speaking not a function. Along the way, I show that for infinite dimensions, a vector space is not necessarily isomorphic to its dual space. Enjoy! Check out my dual space playlist: ht
From playlist Dual Spaces
