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
In this video, I show how to explicitly calculate dual bases. More specifically, I find the dual basis corresponding to the basis (2,1) and (3,1) of R^2. Hopefully this will give you a better idea of how dual bases work. Subscribe to my channel: https://www.youtube.com/c/drpeyam What is
From playlist Dual Spaces
In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. En
From playlist Dual Spaces
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
Duality in Linear Algebra: Dual Spaces, Dual Maps, and All That
An exploration of duality in linear algebra, including dual spaces, dual maps, and dual bases, with connections to linear and bilinear forms, adjoints in real and complex inner product spaces, covariance and contravariance, and matrix rank. More videos on linear algebra: https://youtube.c
From playlist Summer of Math Exposition Youtube Videos
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra
In this video, we solve a classical dual space exercise: Given a set F of linear functionals, find a basis B of V such that F is the dual basis of B. This procedure is very important in applications, an in fact in another video, we'll see a neat application of this idea to numerical integr
From playlist Dual Spaces
Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Phong NGUYEN - Recent progress on lattices's computations 1
This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT
From playlist Summer of Math Exposition 2 videos
Harold Dales: Multi-norms and Banach lattices
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 Analysis and its Applications
2020 Theory Winter School: Srinivas Raghu (pt2)
Topic: Boson-ferimon duality in strongly coupled field theories Part 2 For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
What is the Symmetric Difference of 2 Sets?
What is the symmetric difference of 2 sets? In this video we go over the symmetric difference of sets, explaining it in a couple ways including what is probably the briefest way. The symmetric difference of two sets A and B is (A union B)-(A intersect B). If you need to know what the defin
From playlist Set Theory
Definition of V** (double dual) and an amazing miracle Dual Space Definition: https://youtu.be/OGO3HGlOQO4 Dual Spaces Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCs0fJDQnXgeuyFR8iQDwLV Subscribe to my channel: https://www.youtube.com/c/drpeyam
From playlist Dual Spaces
Lecture 29 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues to lecture on the general stretch theorem and begins covering medical imaging. The Fourier transform is a tool for solving physical p
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Geoffrey Grimmett (University of Cambridge, UK) by Geoffrey Grimmett
PROGRAM FIRST-PASSAGE PERCOLATION AND RELATED MODELS (HYBRID) ORGANIZERS: Riddhipratim Basu (ICTS-TIFR, India), Jack Hanson (City University of New York, US) and Arjun Krishnan (University of Rochester, US) DATE: 11 July 2022 to 29 July 2022 VENUE: Ramanujan Lecture Hall and online This
From playlist First-Passage Percolation and Related Models 2022 Edited
2020 Theory Winter School: Srinivas Raghu
Topic: Boson-ferimon duality in strongly coupled field theories For more information on the 2020 Theory Winter School: https://nationalmaglab.org/news-events/events/for-scientists/winter-theory-school
From playlist 2020 Theory Winter School
N=2* Yang-Mills on the Lattice by Anosh Joseph
Bangalore Area Strings Meeting - 2017 TIME : 31 July 2017 to 02 August 2017 VENUE:Madhava Lecture Hall, ICTS Bangalore Bengaluru now has a large group of string theorists, with 9 faculty members in the area, between ICTS and IISc. This is apart from a large group of postdocs and graduate
From playlist Bangalore Area Strings Meeting - 2017
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