A nice basis for a nilpotent operator. Jordan basis. Jordan form for an operator on a finite-dimensional complex vector space.
From playlist Linear Algebra Done Right
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
GT10. Examples of Non-Isomorphic Groups
EDIT: Fix for 14:10: "Here's a quick way to fix. If y has order 3, then the order of yH divides 3. By assumption, yH has order 2, a contradiction. Recall that yH=H means y is in H. I'm actually overthinking the entire proof. Once we have H, pick any y not in H. Then yxy^-1=x^2.
From playlist Abstract Algebra
Ben Webster - Representation theory of symplectic singularities
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Semirings that are finite and have infinity
Semirings. You can find the simple python script here: https://gist.github.com/Nikolaj-K/f036fd07991fce26274b5b6f15a6c032 Previous video: https://youtu.be/ws6vCT7ExTY
From playlist Algebra
Roland Speicher: Free probability theory - Lecture 1
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: Usual free probability theory was introduced by Voiculescu in the context of operator algebras. It turned out that there exists also a relation to random matri
From playlist Noncommutative geometry meets topological recursion 2021
Linear Algebra 1.6 More on Linear Systems and Invertible 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
From playlist Linear Algebra
Nigel Higson: The Oka principle and Novodvorskii’s theorem
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on November 11, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Chi-Keung Ng: Ortho-sets and Gelfand spectra
Talk by Chi-Keung Ng in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on June 9, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Example of Jordan Canonical Form: 2x2 Matrix
Matrix Theory: Find the Jordan form for the real 2 x 2 matrix A = [0 -4 \ 1 4]. For this matrix, there is no basis of eigenvectors, so it is not similar to a diagonal matrix. One alternative is to use Jordan canonical form.
From playlist Matrix Theory
Dihedral Group (Abstract Algebra)
The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo
From playlist Abstract Algebra
Linear Algebra: Ch 2 - Determinants (23 of 48) Non-Invertible Matrix: Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will find a13=? of a 3x3 matix the determinant of that matrix is non-invertible. Next video in this series can be seen at: https://youtu.be/8uFfoMWgfRc
From playlist LINEAR ALGEBRA 2: DETERMINANTS
Carla Farsi: Proper Lie Groupoids and their structures
Talk by Carla Farsi in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 24, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Transport in RMT - Alice Guionnet
Alice Guionnet ENS Lyon November 6, 2013 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Alex Fok, Equvariant twisted KK-theory of noncompact Lie groups
Global Noncommutative Geometry Seminar(Asia-Pacific), Oct. 25, 2021
From playlist Global Noncommutative Geometry Seminar (Asia and Pacific)
Rainer Verch: Linear hyperbolic PDEs with non-commutative time
Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form (D + sW) f = 0 are studied, where D is a normal or prenormal hyperbolic differential operator on Minkowski spacetime, s is a coupling constant, and W i
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Yuri Kordyukov: Adiabatic limits and noncommutative geometry of foliations
We discuss the asymptotic behavior of the eigenvalues of the Laplacian on a Riemannian compact foliated manifold when the metric is blown up in the directions normal to the leaves (in the adiabatic limit). This problem can be considered as an asymptotic spectral problem on the leaf space
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Linear Algebra 8.6 Geometry of Matrix Operators
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
Andrzej Sitarz: Spectral action for 3+1 geometries
I'll demonstrate a class of models, to illustrate a principle of evolution for 3-dimensional noncommutative geometries, determined exclusively by a spectral action. One particular case is a model, which allows evolution of noncommutativeness (deformation parameter) itself for a specific c
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"