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
In this video I write down the axioms of Lie algebras and then discuss the defining anti-symmetric bilinear map (the Lie bracket) which is zero on the diagonal and fulfills the Jacobi identity. I'm following the compact book "Introduction to Lie Algebras" by Erdmann and Wildon. https://gi
From playlist Algebra
Linear Algebra 7.2 Orthogonal Diagonalization
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
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
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
11I Orthogonal Projection of a Vector
The Orthogonal Projection of one vector along another.
From playlist Linear Algebra
Eigenvectors of Symmetric Matrices Are Orthogonal
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 Part 4 Linear Algebra: Inner Products
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
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
Tobias Braun - Orthogonal Determinants
Basic concepts and notions of orthogonal representations are in- troduced. If X : G → GL(V ) is a K-representation of a nite group G it may happen that its image X(G) xes a non-degenerate quadratic form q on V . In this case X and its character χ : G → K, g 7 → trace(X(g)) are called ortho
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
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
Symmetric spaces (Lecture - 3) by Pralay Chatterjee
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Anna Seigal: "From Linear Algebra to Multi-Linear Algebra"
Watch part 2/2 here: https://youtu.be/f5MiPayz_e8 Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "From Linear Algebra to Multi-Linear Algebra" Anna Seigal - University of Oxford Abstract: Linear algebra is the foundation to methods for finding
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Tensor Calculus Lecture 8: Embedded Surfaces and the Curvature Tensor
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
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
Higgs bundles and higher Teichmüller components (Lecture 2) by Oscar García-Prada
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020