Lecture 27. Properties of tensor products
0:00 Use properties of tensor products to effectively think about them! 0:50 Tensor product is symmetric 1:17 Tensor product is associative 1:42 Tensor product is additive 21:40 Corollaries 24:03 Generators in a tensor product 25:30 Tensor product of f.g. modules is itself f.g. 32:05 Tenso
From playlist Abstract Algebra 2
A Concrete Introduction to Tensor Products
The tensor product of vector spaces (or modules over a ring) can be difficult to understand at first because it's not obvious how calculations can be done with the elements of a tensor product. In this video we give an explanation of an explicit construction of the tensor product and work
From playlist Tensor Products
Representation Theory: We apply character theory to tensor products. We obtain a character formula for general tensor products and, as special cases, alternating and symmetric 2-tensors. As an application, we compute the character table for S4, the symmetric group on 4 letters.
From playlist Representation Theory
What is a Tensor 5: Tensor Products
What is a Tensor 5: Tensor Products Errata: At 22:00 I write down "T_00 e^0 @ e^1" and the correct expression is "T_00 e^0 @ e^0"
From playlist What is a Tensor?
The TRUTH about TENSORS, part 5: ... is something that transforms like a tensor
In the longest video of this series (yet), we review contravariant and covariant vectors, and deriving the transformation law for a multi-linear map on a repeated tensor product of a vector space and its dual. Introduction (0:00) Contravariant vectors (1:33) Dual space (10:24) The transfo
From playlist The TRUTH about TENSORS
Proof: Uniqueness of the Tensor Product
Universal property introduction: https://youtu.be/vZzZhdLC_YQ This video proves the uniqueness of the tensor product of vector spaces (or modules over a commutative ring). This uses the universal property of the tensor product to prove the existence of an isomorphism (linear bijection) be
From playlist Tensor Products
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
What is a Tensor 6: Tensor Product Spaces
What is a Tensor 6: Tensor Product Spaces There is an error at 15:00 which is annotated but annotations can not be seen on mobile devices. It is a somewhat obvious error! Can you spot it? :)
From playlist What is a Tensor?
What is a Tensor? Lesson 29: Transformations of tensors and p-forms (part review)
What is a Tensor? Lesson 29: Tensor and N-form Transformations This long lesson begins with a review of tensor product spaces and the relationship between coordinate transformations on spacetime and basis transformations of tensor fields. Then we do a full example to introduce the idea th
From playlist What is a Tensor?
Anthony Nouy: Approximation and learning with tree tensor networks - Lecture 1
Recorded during the meeting "Data Assimilation and Model Reduction in High Dimensional Problems" the July 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone A kinetic description of a plasma in external and self-consistent fiel
From playlist Numerical Analysis and Scientific Computing
Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I
Lie Groups and Lie Algebras: Lesson 41: Elementary Representation Theory I I wanted to begin a more intricate example of the principle of a Universal Covering group, but I think I need to cover a little background material. We need to get a grip on what is meant by "Representation Theory"
From playlist Lie Groups and Lie Algebras
Rings 11 Tensor products of modules
This lecture is part of an online course on rings and modules. We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
From playlist Rings and modules
Kazhdan-Lusztig equivalence - Pablo Boixeda Alvarez
Quantum Groups Seminar Topic: Kazhdan-Lusztig equivalence Speaker: Pablo Boixeda Alvarez Affiliation: Member, School of Mathematics Date: May 13, 2021 For more video please visit https://www.ias.edu/video
From playlist Quantum Groups Seminar
Webs in type C - Benjamin Elias
Workshop on Representation Theory and Geometry Topic: Webs in type C Speaker: Benjamin Elias Affiliation: University of Oregon; von Neumann Fellow, School of Mathematics Date: March 31, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - M.Brannan
Michael Brannan (College station) / 12.09.17 Title: Entangled subspaces from quantum groups and their associated quantum channels. Abstract:I will describe a class of highly entangled subspaces of bipartite quantum systems arising from the representation theory of a class of compact quan
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Oct. 8, Chapter 9 (Tensor Products)
From playlist Fall 2020 Course
Frobenius exact symmetric tensor categories - Pavel Etingof
Geometric and Modular Representation Theory Seminar Topic: Frobenius exact symmetric tensor categories Speaker: Pavel Etingof Affiliation: Massachusetts Institute of Technology Date: May 12, 2021 For more video please visit https://www.ias.edu/video
From playlist Seminar on Geometric and Modular Representation Theory
Francesca Arici: SU(2)-symmetries and exact sequences of C*-algebras through subproduct systems
Talk by Francesca Arici in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on November 17, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Commutative algebra 20 Tensor products review
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 review the definition of the tensor product of R-modules. We calculate the tensor products in the cases of
From playlist Commutative algebra