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
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
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From playlist Science Unplugged: Special Relativity
Null Space and Column Space of a Matrix
Given a matrix A(ie a linear transformation) there are several important related subspaces. In this video we investigate the Nullspace of A and the column space of A. The null space is the vectors that are "killed" by the transformation - ie sent to zero. The column space will be the image
From playlist Older Linear Algebra Videos
In this video we define a metric space. - Please note that a portion of this video has been removed due to an error. 0:00 - Distance function 4:01 - Metric Space (definition) The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking th
From playlist Approximation Theory
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
Large deviations for the Wiener Sausage by Frank den Hollander
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
WildLinAlg17: Rank and Nullity of a Linear Transformation
We begin to discuss linear transformations involving higher dimensions (ie more than three). The kernel and the image are important spaces, or properties of vectors, associated to a linear transformation. The corresponding dimensions are the nullity and the rank, and they satisfy a simple
From playlist A first course in Linear Algebra - N J Wildberger
Large deviations for the Wiener Sausage (Lecture 2) by Frank den Hollander
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
5.01 Van Kampen's theorem: statement and examples
We formulate Van Kampen's theorem and use it to calculate some fundamental groups. For notes, see here: http://www.homepages.ucl.ac.uk/~ucahjde/tg/html/vkt01.html
From playlist Algebraic Topology
Yair Shenfeld - The Brownian transport map - IPAM at UCLA
Recorded 09 February 2022. Yair Shenfeld of the Massachusetts Institute of Technology presents "The Brownian transport map" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The existence of Lipschitz transport maps between probability measures leads to tran
From playlist Workshop: Calculus of Variations in Probability and Geometry
Go to https://NordVPN.com/nilered and or use code NILERED to to get 75% off a 3 year plan. Protect yourself online today! ---------------------------------------------- Correction: at 12:50 I said that pure nitrogen is denser than air, but that isn't true. The specific gravity of nitroge
From playlist Mercury
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
Emily Stark: Action rigidity for free products of hyperbolic manifold groups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
Lec 16 | MIT 18.085 Computational Science and Engineering I
Dynamic estimation: Kalman filter and square root filter A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
Modulation Spaces and Applications to Hartree-Fock Equations by Divyang Bhimani
We discuss some ongoing interest (since last decade) in use of modulation spaces in harmonic analysis and its connection to nonlinear dispersive equations. In particular, we shall discuss results on Hermite multiplier and composition operators on modulation spaces. As an application to the
From playlist ICTS Colloquia
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Specialization of difference equations ... - H. Hrushovski - Workshop 2 - CEB T1 2018
Michael Temkin (Hebrew University) / 06.03.2018 Specialization of difference equations in positive characteristic. A difference equation over an increasing transformal valued field is known to beanalyzable over the residue field. This leads to a dynamical theory of equivalence of finite
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Introduction to Fiber Bundles Part 3: Associated Bundles and Amalgamated Products
This is an incomplete introduction here. The basic idea is that the associated principal bundle knows all. This should be obvious since all bundles with G-structure are classified by H^1(X,G) --- it turns out you can recover your original bundle from a principal bundle by taking "amalgamat
From playlist Fiber bundles
What is General Relativity? Lesson 5: The Catalogue of Spacetimes
What is General Relativity? Lesson 5: The Catalogue of Spacetimes - Minkowski Spacetime I invite you to download the Catalog of Spacetimes at : https://arxiv.org/abs/0904.4184 to use as a reference for the rest of the course.
From playlist What is General Relativity?