Linear transformation with given range
Fun exercise in linear algebra: Given a subspace Z, find a linear transformation whose range/image is Z. Great illustration of the definition of a basis and the Linear Extension Theorem. Enjoy! Linear Extension Theorem: https://youtu.be/gAlUekIYKLA Check out my Linear Transformations Pl
From playlist Linear Transformations
Extend a linearly independent set to a basis In this video, I show how to concretely extend any linearly independent subset of a vector space to a basis of that vector space. We know we can do that in theory (using the replacement theorem), but this video shows how to do it in concrete si
From playlist Linear Equations
Linear algebra: Prove the Sherman-Morrison formula for computing a matrix inverse
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
In this video, I prove one of the cornerstones of linear algebra: The Linear Extension Theorem, which intuitively says that, in order to define a linear transformation T, you only need to know the values of T on a basis. In other words, if you only know T on a couple of vectors, you can ac
From playlist Linear Transformations
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
In this video, I show that two vector spaces are isomorphic if and only if they have the same dimension. This is an important fact in linear algebra. The proof is very cute and uses the linear extension theorem which I talked about in another video. Enjoy! Linear Extension Theorem https:/
From playlist Linear Transformations
Linear Algebra 8.2 Compositions and Inverse Transformations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=KlAjiDivJoQ&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
V8-8: Properties of Fourier series, linearity and convergence. Elementary Differential Equations
Properties of Fourier series, linearity and convergence. Examples. Elementary Differential Equations Course playlist: https://www.youtube.com/playlist?list=PLbxFfU5GKZz0GbSSFMj
From playlist Elementary Differential Equations
Seffi Naor: Recent Results on Maximizing Submodular Functions
I will survey recent progress on submodular maximization, both constrained and unconstrained, and for both monotone and non-monotone submodular functions. The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization.
From playlist HIM Lectures 2015
Matthias Seiß, Universität Kassel
April 16, Matthias Seiß, Universität Kassel Differential Invariants and the Classical Groups
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Elias Khalil - Neur2SP: Neural Two-Stage Stochastic Programming - IPAM at UCLA
Recorded 02 March 2023. Elias Khalil of the University of Toronto presents "Neur2SP: Neural Two-Stage Stochastic Programming" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Stochastic Programming is a powerful modeling framework for decision-making under un
From playlist 2023 Artificial Intelligence and Discrete Optimization
Mihalis Dafermos - The "inside story" of black hole stability
The "inside story" of black hole stability Licence: CC BY NC-ND 4.0
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Lecture with Ole Christensen. Kapitler: 00:00 - Def.: Closure Of A Subset; 06:45 - Dense Vs. Closure; 19:00 - Extension Of Operators On Dense Subspaces; 24:15 - Proof;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Stefanie Jegelka - Two aspects of learning algorithms: generalization under shifts & loss functions
Recorded 02 March 2023. Stefanie Jegelka of the Massachusetts Institute of Technology presents "Two aspects of learning algorithms: generalization under shifts and loss functions" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Graph Neural Networks (GNNs) h
From playlist 2023 Artificial Intelligence and Discrete Optimization
Linear Transformations and Linear Systems
In this video we discuss linear transformations. We start by examining the mathematical definition of a linear transformation and apply it to several examples including matrix multiplication and differentiation. We then see how linear transformations relate to linear systems (AKA linear
From playlist Linear Algebra