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
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
Ex 2: Properties of Cross Products - Cross Product of a Sum and Difference
This video explains how to find the cross product of a sum and difference of two vectors. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
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?
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
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?
Ex 1: Properties of Cross Products - Cross Product of a Sum and Difference
This video explains how to find the cross product of a sum and difference of two vectors. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
There are two types of vector multiplication. In this tutorial we take a look at the vector dot product, also known as the vector inner product. The result of a vector inner product is a scalar. There are two ways to calculate this scalar, which can help us to determine the angle betwee
From playlist Introducing linear algebra
Nonlinear algebra, Lecture 8: "Tensors", by Bernd Sturmfels and Mateusz Michalek
This is the eight lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
What is a Tensor Lesson 27: Formal development of p-forms and p-vectors Part I
What is a Tensor? Lesson 27: Formal development of p-forms and p-vectors (Part I) This is the first of a short series where we dig into the more formal presentation of p-forms and p-vectors. I am doing these to be complete and give those who are reading more technical books on the subject
From playlist What is a Tensor?
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)
Tensor Calculus Lecture 9a: The Equations of Surface and the Shift 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
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”
Stanislaw Szarek: The projective/injective ratio and GPTs
Among natural tensor products of normed spaces, the projective and the injective are the extreme ones. The question : How much do they differ? was considered by Grothendieck and Pisier (in the 1950s and 1980s), but - surprisingly - no systematic quantitative analysis of the finite- dimensi
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Relative Error Tensor Low Rank Approximation by David Woodruff
Statistical Physics Methods in Machine Learning DATE:26 December 2017 to 30 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "th
From playlist Statistical Physics Methods in Machine Learning
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
Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
From playlist What is a Tensor?
Anthony Nouy: Approximation and learning with tree tensor networks - Lecture 2
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