Dual object

Duality Argument

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

Dual Space

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

Dual basis

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

Dual Basis Example

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

Double Dual

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

Every basis is a dual basis

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

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

Transpose Definition

Definition of the transpose Have you ever wondered where the transpose comes from? In this video, I show that the transpose arises naturally in the setting of dual spaces. This should also illustrate why dual spaces are so important. Enjoy! Transpose Example (Sequel): https://youtu.be/x2

From playlist Dual Spaces

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

Delayed column generation in large scale integer optimization problems - Professor Raphael Hauser

Mixed linear integer programming problems play an important role in many applications of decision mathematics, including data science. Algorithms typically solve such problems via a sequence of linear programming approximations and a divide-and-conquer approach (branch-and-bound, branch-an

From playlist Data science classes

An introduction to modified traces, Jonathan Kujawa, Lecture I

Lecture series on modified traces in algebra and topology The trace of a map and the dimension of a representation are fundamental invariants in representation theory. They are useful both for proving results in representation theory and for applications in other areas (e.g., low-dimensio

From playlist Lecture series on modified traces in algebra and topology

Duality In Higher Categories IV by Pranav Pandit

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Linear Programming, Lecture 15. Definition of dual problem. Examples.

Penn State University. Oct 13, 2016.

From playlist Math484, Linear Programming, fall 2016

Niles Weed :Weak limits for entropic optimal transport II

CONFERENCE Recording during the thematic meeting : "Meeting in Mathematical Statistics " the December 15, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on

From playlist Probability and Statistics

What is a Tensor 4: Cartesian Products

What is a Tensor 4: Cartesian Products

From playlist What is a Tensor?

IE513 20110418 LECTURE30 Duality theorems

From playlist Bilkent: IE 513 | CosmoLearning.org

IE513 20110406 LECTURE29 Duality cont'd

From playlist Bilkent: IE 513 | CosmoLearning.org

Categorical joins - Alex Perry

Workshop on Homological Mirror Symmetry: Methods and Structures Title: Categorical joins Speaker: Alex Perry Affiliation: Harvard Date: November 7, 2016 For more video, visit http://video.ias.edu

From playlist Mathematics

Proving that two functions are not inverses of each other

👉 Learn how to show that two functions are inverses. The composition of two functions is using one function as the argument (input) of another function. In simple terms composition of two functions is putting one function inside another function. The composition of two functions that are i

From playlist Find the Inverse of a Function

Lecture 8 | Convex Optimization I (Stanford)

Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on duality in the realm of electrical engineering and how it is utilized in convex optimization for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizi

From playlist Lecture Collection | Convex Optimization