Riemannian geometry | Tensors | Connection (mathematics)
The contorsion tensor in differential geometry is the difference between a connection with and without torsion in it. It commonly appears in the study of spin connections. Thus, for example, a vielbein together with a spin connection, when subject to the condition of vanishing torsion, gives a description of Einstein gravity. For supersymmetry, the same constraint, of vanishing torsion, gives (the field equations of) 11-dimensional supergravity. That is, the contorsion tensor, along with the connection, becomes one of the dynamical objects of the theory, demoting the metric to a secondary, derived role. The elimination of torsion in a connection is referred to as the absorption of torsion, and is one of the steps of Cartan's equivalence method for establishing the equivalence of geometric structures. (Wikipedia).
Calculus 3: Tensors (13 of 45) What is the Inertia Tensor?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the inertia tensor relating the physical inertia activity and the tensor component notation. Next video in the series can be seen at: https://youtu.be/-chgCHuEI4Y
From playlist CALCULUS 3 CH 10 TENSORS
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
Calculus 3: Tensors (16 of 45) The Complete Inertia Tensor
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the complete inertia tensor matrix containing 9 elements consisting the diagonal elements and off-diagonal elements. Next video in the series can be seen at: https://youtu.be/4vjAuWarmQM
From playlist CALCULUS 3 CH 10 TENSORS
Amazing Art and MORE! IMG! #49
Follow us @tweetsauce Share IMG!s, DONGs, and more at http://www.Facebook.com/VsauceGaming music at the end by http://www.Soundcloud.com/JakeChudnow bearded babies: http://worldwideinterweb.com/component/joomgallery/funny/babies-with-beards/baby-facial-hair-222.html#joomimg cup of kitt
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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
What is a Tensor? Lesson 18: The covariant derivative continued
What is a Tensor? Lesson 18: The covariant derivative continued This lesson covers some of the "coordinate free" language used to describe the covariant derivative. As a whole this lecture is optional. However, becoming comfortable with coordinate free language is probably a good idea. I
From playlist What is a Tensor?
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
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
What is General Relativity? Lesson 68: The Einstein Tensor
What is General Relativity? Lesson 68: The Einstein Tensor The Einstein tensor defined! Using the Ricci tensor and the curvature scalar we can calculate the curvature scalar of a slice of a manifold using the Einstein tensor. Please consider supporting this channel via Patreon: https:/
From playlist What is General Relativity?
Calculus 3: Tensors (18 of 45) The Inertia Tensor: A LESS Simple Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the 9 components of a LESS simple example (mass of m=1 is place on the xy-plane (1,1,0)) of an inertia tensor matrix. Next video in the series can be seen at: https://youtu.be/9jOrDufoO50
From playlist CALCULUS 3 CH 10 TENSORS
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
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
Anna Seigal: "From Linear Algebra to Multi-Linear Algebra"
Watch part 2/2 here: https://youtu.be/f5MiPayz_e8 Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "From Linear Algebra to Multi-Linear Algebra" Anna Seigal - University of Oxford Abstract: Linear algebra is the foundation to methods for finding
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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
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?
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?
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?
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
Tensor Calculus for Physics Ep. 9 | Derivatives of Tensors, and the Affine Connection
Is the derivative of a tensor a tensor? Find out now on dragon ball z. We also derive the geodesic equation. https://www.amazon.com/gp/product/1421415658/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1421415658&linkCode=as2&tag=andrewdotson-20&linkId=b45243268a957a6cfdfc854a8f
From playlist New To Tensors? Start Here