In graph theory, the tensor product G × H of graphs G and H is a graph such that * the vertex set of G × H is the Cartesian product V(G) × V(H); and * vertices (g,h) and (g',h' ) are adjacent in G × H if and only if * g is adjacent to g' in G, and * h is adjacent to h' in H. The tensor product is also called the direct product, Kronecker product, categorical product, cardinal product, relational product, weak direct product, or conjunction. As an operation on binary relations, the tensor product was introduced by Alfred North Whitehead and Bertrand Russell in their Principia Mathematica. It is also equivalent to the Kronecker product of the adjacency matrices of the graphs. The notation G × H is also (and formerly normally was) used to represent another construction known as the Cartesian product of graphs, but nowadays more commonly refers to the tensor product. The cross symbol shows visually the two edges resulting from the tensor product of two edges. This product should not be confused with the strong product of graphs. (Wikipedia).
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
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?
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
Cross Product and Dot Product: Visual explanation
Visual interpretation of the cross product and the dot product of two vectors. My Patreon page: https://www.patreon.com/EugeneK
From playlist Physics
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?
Multivariable Calculus | The dot product.
We present the definition of the dot product as well as a geometric interpretation and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
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
Anna Seigal: "Tensors in Statistics and Data Analysis"
Watch part 1/2 here: https://youtu.be/9unKtBoO5Hw Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensors in Statistics and Data Analysis" Anna Seigal - University of Oxford Abstract: I will give an overview of tensors as they arise in settings
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogu
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
Unveiling the Power of Graphs: Node and Edge Classification w/ GraphSAGE | GraphML
Full code example of Node and Edge classification with GraphSAGE for GraphML. DGL on PyTorch backbone. Graph Neural Networks explained. One of the most popular and widely adopted tasks for graph neural networks is node classification, where each node in the training/validation/test set is
From playlist Node & Edge Classification, Link Prediction w/ GraphML
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
Asymptotic spectra and Applications I - Jeroen Zuiddam
Computer Science/Discrete Mathematics Seminar I Topic: Asymptotic spectra and Applications I Speaker: Jeroen Zuiddam Affiliation: Member, School of Mathematics Date: October 8, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Richard Kueng: "Predicting Many Properties of a Quantum System From Very Few Measurements"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Predicting Many Properties of a Quantum System From Very Few Measurements" Richard Kueng - Johannes Kepler University A
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Calculus 3: Tensors (1 of 28) What is a Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t
From playlist CALCULUS 3 CH 10 TENSORS
Live CEOing Ep 654: Language Design in Wolfram Language [Multicomputation]
In this episode of Live CEOing, Stephen Wolfram discusses upcoming improvements and features to the Wolfram Language. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram
From playlist Behind the Scenes in Real-Life Software Design
Random Vectors, Random Matrices, Permuted Products, Permanents, and Diagrammatic Fun - Moore
Cris Moore Santa Fe Institute October 1, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Singular Values of Tensors
From playlist Spring 2019 Symbolic-Numeric Computing
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