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
What is the Alternate Exterior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
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
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
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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
What is the Alternate Interior Angle Converse Theorem
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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)
Developments in 4-manifold topology arising from a theorem of Donaldson's - John Morgan [2017]
slides for this talk: https://drive.google.com/file/d/1_wHviPab9klzwE4UkCOvVecyopxDsZA3/view?usp=sharing Name: John Morgan Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: Developments in 4-manifold topology arising from a theorem of Donaldson's Date: 2017-10-23 @9:3
From playlist Mathematics
Jeff Erickson - Lecture 3 - Two-dimensional computational topology - 20/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Jeff Erickson (University of Illinois at Urbana-Champaign, USA) Two-dimensional computational topology - Lecture 3 Abstract: This series of lectures will describe recent
From playlist Jeff Erickson - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Quantization by Branes and Geometric Langlands (Lecture 4) 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 Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
MAST30026 Lecture 19: Duality and Hilbert space
I began by proving the universal property of the completion of a normed space. I then discussed characterisations of finite-dimensionality for vector spaces, introduced the continuous linear dual for normed spaces and the operator norm, and stated the duality theorem or L^p spaces which sa
From playlist MAST30026 Metric and Hilbert spaces
Dustin Clausen: New foundations for functional analysis
Talk by Dustin Clausen in Global Noncommutative Geometry Seminar (Americas) on November 12, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Foundations of QM: Introduction Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussing the material on the forums: https://www.patreon.com/XYLYXYLYX
From playlist Mathematical Foundations of Quantum Mechanics
Séverin Charbonnier: Topological recursion for fully simple maps
Talk at the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Fully simple maps show strong relations with symplectic invariance of topological recursion and free probabilities. While ordinary maps satisfy topological recursion
From playlist Noncommutative geometry meets topological recursion 2021
Summing Over Bordisms In 2d TQFT - Greg Moore
Black Holes and Qubits Meeting Topic: Summing Over Bordisms In 2d TQFT Speaker: Greg Moore Affiliation: Rutgers University Date: March 24, 2022 Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms betwee
From playlist Natural Sciences
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology