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
A variation on an Ulam Spiral: a Sacks Spiral
Simplicity making complexity. In one word: Emergence. Using the same process as my Ulam Spiral video, https://youtu.be/JjBnLz0SF3A but this time in a Sacks Spiral, https://youtu.be/iFuR97YcSLM?t=6m3s Enjoy. Animation made with FMS Logo.
From playlist Artsy things
What is a Tensor? Lesson 31: Tensor Densities (Part 2 of Tensor Transformations)
This video is about What is a Lesson 31: Tensor Densities (Part 2 of Tensor Transformations) We introduce the *classical* definition of a tensor density and connect that definition to our more robust approach associated with vector spaces and their associated bases. I will demonstrate som
From playlist What is a Tensor?
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras We complete our survey of the basic algebraic structures that appear in the study of general relativity. Also, we develop the important example of the tensor algebra.
From playlist What is a Tensor?
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
The TRUTH about TENSORS, Part 10: Frames
What do the octonions have to do with spheres? Skip to the end of the video to find out!
From playlist The TRUTH about TENSORS
Linear Algebra 4e: Linear Subspaces in ℝⁿ
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
The TRUTH about TENSORS, Part 2: Free Bugaloo
In this video we write down the definition of free modules in terms of a universal property, and prove that it exists.
From playlist The TRUTH about TENSORS
3.9 - More Expressivity with Web Ontology Language - OWL
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 9: Knowledge Graphs - 4 3.9 More Expressivity with Web Ontology Language - OWL - OWL 2 flavours - OWL 2 DL and Description Logics - Simple classes and properties in O
From playlist ISE2021 - Lecture 09, 16.06.2021
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
Part 3 of the series on the Crusades. An overview of the human, territorial, commercial and political impact of the Crusades.
From playlist 600 - 1450 Regional and interregional interactions | AP World History | Khan Academy
23 - More examples of subspaces
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
3.9c - More Expressivity with Web Ontology Language - OWL 3
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 9: Knowledge Graphs - 4 3.9c More Expressivity with Web Ontology Language - OWL complex properties - OWL property chains - Limits of OWL Playlist: https://www.youtub
From playlist ISE2021 - Lecture 09, 16.06.2021
5.3+ - Hands on Data Acquisition
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 13: ISE Applications - 1 5.3+ Hands-on Data Acquisition - How to get the Data from DBpedia / Wikidata - Wikidata Recap (Namespaces for statements and qualifiers) Pla
From playlist ISE2021 - Lecture 13 - 14.07.2021
4.10 - Knowledge Graph Embeddings
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 12: Basic Machine Learning 3 4.10 - Knowledge Graph Embeddings - distributed semantics - graph embeddings - knowledge graph embeddings - knowledge graph completion -
From playlist ISE2021 - Lecture 12 - 07.07.2021
3.9b - More Expressivity with Web Ontology Language - OWL 2
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 9: Knowledge Graphs - 4 3.9b More Expressivity with Web Ontology Language - OWL complex class definitions - OWL property restrictions - OWL Strict binding and loose b
From playlist ISE2021 - Lecture 09, 16.06.2021
03.6b - Logical Inferences with RDFS
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture7: Knowledge Graphs - 2 3.6b Logical Inferences with RDFS - RDFS Semantics - Inferences with RDFS Playlist: https://www.youtube.com/playlist?list=PLNXdQl4kBgzuuZZkIT
From playlist ISE 2021 - Lecture 07, 02.06.2021
09 - ISE2021 - Lecture 09 Trailer
Information Service Engineering 2021 Prof. Dr. Harald Sack Karlsruhe Institute of Technology Summer semester 2021 Lecture 9: Knowledge Graphs - 4 Lecture 09 Trailer 3.9 More Expressivity with Web Ontology Language (OWL) 3.9b More Expressivity with Web Ontology Language (OWL) 2 3.9c More
From playlist ISE2021 - Lecture 09, 16.06.2021
What Is A Tensor Lesson #1: Elementary vector spaces
We define a vector space and lay the foundation of a solid understanding of tensors.
From playlist What is a Tensor?