The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Linear Algebra 7.1 Orthogonal Matrices
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
Orthogonal complements. The direct sum of a subspace and its orthogonal complement. Dimension of the orthogonal complement. The orthogonal complement of the orthogonal complement.
From playlist Linear Algebra Done Right
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q)
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q) In this lecture we back up and deploy the basis elements we eliminated in the su(2) and so(3) algebras when we enforced the determinants to be equal to 1. This expands the algebras to u(2) and o(3) and generates the groups U(2) a
From playlist Lie Groups and Lie Algebras
11I Orthogonal Projection of a Vector
The Orthogonal Projection of one vector along another.
From playlist Linear Algebra
Lie groups: Lie groups and Lie algebras
This lecture is part of an online graduate course on Lie groups. We discuss the relation between Lie groups and Lie algebras, and give several examples showing how they behave differently. Lie algebras turn out to correspond more closely to the simply connected Lie groups. We then explain
From playlist Lie groups
Lie Groups for Deep Learning w/ Graph Neural Networks
Lie Groups encode the symmetry of systems. We examine actions of a Lie group on a vector space, given their algebraic, topological and analysis based connectome. Deep Learning algorithms for Graph Neural Networks (GNN) are non trivial, and to understand them Lie Groups are essential! A r
From playlist Learn Graph Neural Networks: code, examples and theory
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux)
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux) We name the classical groups, finally! This video ended a bit short, I added the missing part in the "redux" version of this lesson. Please consider supporting this channel via Patreon: https://www.patreon.com/
From playlist Lie Groups and Lie Algebras
Fabrizio Andreatta: Integral canonical models of orthogonal Shimura varieties
Fabrizio Andreatta: Integral canonical models of orthogonal Shimura varieties. A proof of a conjecture of Bruinier and Yang Let (V,Q) be a quadratic space over Q with signature (2, n) and let L \subset V be a perfect lattice I will define the Shimura variety associated to the algebraic gr
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Linear Algebra - Lecture 38 - Orthogonal Sets
In this lecture, we discuss orthogonal sets of vectors. We also investigate the idea of an orthogonal basis, as well as orthogonal projections of vectors.
From playlist Linear Algebra Lectures
Vector Calculus 13: Projection onto a Subspace
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
Steven Bradlow - Exotic components of surface group representation varieties
Steven Bradlow Exotic components of surface group representation varieties, and their Higgs bundle avatars Moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. For representations into complex semisimple Lie groups,
From playlist Maryland Analysis and Geometry Atelier
Linear Algebra 3.3 Orthogonality
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
From playlist Linear Algebra
Lie Groups and Lie Algebras: Lesson 33 - Recap of Parameter spaces (with fix at 10:32)
Lie Groups and Lie Algebras: Lesson 33 - Recap of Parameter spaces (Corrected) This lecture has a short text overlay to bridge a missing scene and is corrected from the original. No substantive changes. The added text is at 10:52 and that is the only change. In this video we do a review/r
From playlist Lie Groups and Lie Algebras