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
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
Complete Derivation: Universal Property of the Tensor Product
Previous tensor product video: https://youtu.be/KnSZBjnd_74 The universal property of the tensor product is one of the most important tools for handling tensor products. It gives us a way to define functions on the tensor product using bilinear maps. However, the statement of the universa
From playlist Tensor Products
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
Miles Stoudenmire: "Tensor Networks for Machine Learning and Applications"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop I: Tensor Methods and their Applications in the Physical and Data Sciences "Tensor Networks for Machine Learning and Applications" Miles Stoudenmire - Flatiron Institute Abstract: Tensor networks are
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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?
Tensor Product Basis With the Universal Property
Tensor product universal property explanation: https://youtu.be/vZzZhdLC_YQ Generating set proof: https://youtu.be/KnSZBjnd_74?t=1437 timestamp 23:57 If we have a basis for each of two vector spaces (or modules over a commutative ring) V and W, then we can use that to form a basis for the
From playlist Tensor Products
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?
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
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
Alessandra Bernardi: "On the Dimension of Tensor Network Varieties"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "On the Dimension of Tensor Network Varieties" Alessandra Bernardi - Università di Trento Abstract: I discuss the proble
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
An invitation to tensor networks - Michael Walter
Computer Science/Discrete Mathematics Seminar II Topic: An invitation to tensor networks Speaker: Michael Walter Affiliation: University of Amsterdam Date: December 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Introduction to Tensor Networks (Tutorial) by Philippe Corboz
PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In
From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)
On Expressiveness and Optimization in Deep Learning - Nadav Cohen
Members' Seminar Topic: On Expressiveness and Optimization in Deep Learning Speaker: Nadav Cohen Affiliation: Member, School of Mathematics Date: April 2, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Philippe CORBOZ - Simulation of 2D strongly correlated systems...
Simulation of 2D strongly correlated systems with infinite projected entangled-pair states https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
Time evolution of many-body localized systems in two spatial dimensions by Augustine Kshetrimayum
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
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
Tobias J. Osborne: Towards effective conformal field theories for tensor network states
Tobias J. Osborne: Towards effective conformal field theories for tensor network states Abstract: Recently, building on new ideas in quantum information theory emerging from the study of quantum entanglement, expressive variational classes of quantum states known as tensor network states
From playlist HIM Lectures: Trimester Program "Von Neumann Algebras"