Tensors as a Sum of Symmetric and Antisymmetric Tensors
In the last tensor video, I mentioned second rank tensors can be expressed as a sum of a symmetric tensor and an antisymmetric tensor. Today we prove that.
From playlist New To Tensors? Start Here
The TRUTH about TENSORS, Part 4: The Multiverse
In this video, I sketch the details of the proof that tensor products are commutative and associative. I then define multi-linear maps, which are essential for future videos. Commutativity: (0:00) Associativity: (5:40) Multi-linearity: (15:18)
From playlist The TRUTH about TENSORS
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
Lek-Heng Lim: "What is a tensor? (Part 1/2)"
Watch part 2/2 here: https://youtu.be/Lkpmd5-mpHY Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "What is a tensor? (Part 1/2)" Lek-Heng Lim - University of Chicago, Statistics Abstract: We discuss the three best-known definitions of a tensor:
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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
Matrix Theory: Let T: R^4 to R^4 be the linear transformation that sends v to Av where A = [0 0 0 -1 \ 1 0 0 0 \ 0 1 0 -2 \ 0 0 1 0]. Find all subspaces invariant under T.
From playlist Matrix Theory
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
Tensor Calculus 5b: Invariants Are Tensors
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
Lec 08. Einstein's General Relativity and Gravitation: General Relativity 4
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 08. Einstein's General Relativity and Gravitation -- General Relativity -- Part 4 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W. Ha
From playlist Einstein's General Relativity and Gravitation
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?
Harm Derksen: "Invariant Tensors and Wheeled PROPs"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Invariant Tensors and Wheeled PROPs" Harm Derksen - Northeastern University, Mathematics Abstract: If we take a tensor
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Joseph Landsberg: "Geometry associated to tensor network states"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "Geometry associated to tensor network states" Joseph Landsberg (Clay Scholar) - Texas A&M University - College Station Abstract: I will discuss geometric i
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Tensor Calculus Lecture 13a: Integration - The Arithmetic Integral
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
Tensor Calculus Lecture 8c: The Curvature Tensor On The Sphere Of Radius R
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
GPDE Workshop - Alexakis' theorem on conformally invariant integrals - Charles Fefferman
Charles Fefferman Princeton University February 25, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
Tensors Explained Intuitively: Covariant, Contravariant, Rank
Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
What is General Relativity? Lesson 49: Constructing the Weyl tensor I
What is General Relativity? Lesson 49: Constructing the Weyl tensor I We calculate the conformally invariant part of the Riemann tensor. This is a complex calculation that is not generally done in textbooks. The motivation for the Weyl tensor will come in a later lesson, but I think the d
From playlist What is General Relativity?
Tensor Calculus Lecture 14b: Examples of Curves in 3D
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
Lec 03. Einstein's General Relativity and Gravitation: Special Relativity 2
UCI Physics 255 Einstein's General Relativity and Gravitation (Spring 2014) Lec 03. Einstein's General Relativity and Gravitation -- Special Relativity -- Part 2 View the complete course: http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html Instructor: Herbert W. Ha
From playlist Einstein's General Relativity and Gravitation
Tensor Calculus For Physics Majors 004| Transformation of Two Index Tensors
In this video I go over transformation of two-index tensors, and verify the transformation by taking the transformation of a component of the inertia tensor as an example. Link to Tensor Calculus for Physics Book: https://www.amazon.com/gp/product/1421415658/ref=as_li_tl?ie=UTF8&camp=1789
From playlist New To Tensors? Start Here