Matrix Theory: Let A be an nxn matrix with complex entries. We show that the commutant of A has dimension greater than or equal to n. The key step is to show the result for the Jordan canonical form of A.
From playlist Matrix Theory
You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.
From playlist Abstract algebra
Commutative algebra 53: Dimension Introductory survey
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:
From playlist Commutative algebra
When Does Exponentiation Commute? (Part 1)
In this video, I'll show how one can find pairs of numbers that can be commuted under exponentiation. That is, we can find pairs of numbers such that x^y = y^x. We will take this equation, x^y = y^x and parametrize it to find these (x,y) pairs. It turns out that there are infinitely many n
From playlist Math
Commutative and Associative Properties
My two favorite properties: the commutative and associative properties of multiplication and addition
From playlist Arithmetic
5B Commutative Law of Matrix Multiplication-YouTube sharing.mov
A closer look at three examples of the Commutative Law of Matrix Multiplication.
From playlist Linear Algebra
Canonical Commutation Relation
We discuss the canonical commutation relation between position and momentum operators in quantum mechanics.
From playlist Quantum Mechanics Uploads
Commutative algebra 21 Tensor products and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we study when taking tensor product preserves exactness. We also show that tensor products preserve direct lim
From playlist Commutative algebra
Commutative algebra 44 Flat modules
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We summarize some of the properties of flat modules. In particular we show that for finitely presented modules over local ring
From playlist Commutative algebra
ITHT: Part 9- The Homotopy Category
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheHomotopyCategory Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Nam
From playlist Introduction to Homotopy Theory
Gilles Pisier - Propriétés de relèvement pour les 𝐶^∗-algèbres : du local au global ?
The main problem we will consider is whether the local lifting property (LLP) of a $C^*$-algebra implies the (global) lifting property (LP). Kirchberg showed that this holds if the Connes embedding problem has a positive solution, but it might hold even if its solution is negative. We will
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
A Gentle Approach to Crystalline Cohomology - Jacob Lurie
Members’ Colloquium Topic: A Gentle Approach to Crystalline Cohomology Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: February 28, 2022 Let X be a smooth affine algebraic variety over the field C of complex numbers (that is, a smooth submanifold of C^n which can
From playlist Mathematics
Matrix stability of crystallographic groups - Soren Eilers
Stability and Testability Topic: Matrix stability of crystallographic groups Speaker: Soren Eilers Affiliation: University of Copenhagen Date: February 17, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Canonical lifts in families by James Borger
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
Digression: The cotangent complex and obstruction theory
We study the cotangent complex more in depth and explain its relation to obstruction theory. As an example we construct the Witt vectors of a perfect ring. This video is a slight digression from the rest of the lecture course and could be skipped. Feel free to post comments and questions
From playlist Topological Cyclic Homology
Gilles Pisier: The lifting property for C*-algebras
Talk by Gilles Pisier in Global Noncommutative Geometry Seminar (Americas) on January 14, 2022 in https://globalncgseminar.org/talks/the-lifting-property-for-c-algebras/
From playlist Global Noncommutative Geometry Seminar (Americas)
Commutative algebra 4 (Invariant theory)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture is an informal historical summary of a few results of classical invariant theory, mainly to show just how complic
From playlist Commutative algebra
Derived structures controlling representations - Carl Wang-Erickson
More videos on http://video.ias.edu
From playlist Mathematics