Tensor Analysis and Applications
Tensors are used in various areas of mathematics and physics, particularly in theoretical calculations involving fields in vector spaces. The Einstein's summation convention implies summation over the dummy indices that appear twice in a term as in matrix-matrix or matrix-vector products.
From playlist Wolfram Technology Conference 2021
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
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
In this video I talk about a beautiful family of adjoint functors between module categories, and how these offer a natural inspiration for the definitions of induced representation, and Frobenius reciprocity.
From playlist Miscellaneous Questions
Sequential Spectra- PART 2: Preliminary Definitions
We cover one definition of sequential spectra, establish the smash tensoring and powering operations, as well as some adjunctions. Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu"
From playlist Sequential Spectra
ITHT: Part 11- Quillen Adjunctions
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#QuillenAdjunctions Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub... Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Na
From playlist Introduction to Homotopy 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
What is a Tensor? Lesson 33/34: Duality and Hodge Duality
What is a Tensor? Lesson 33/34: Duality and Hodge Duality This is a long lecture, so it should be split into two parts. The first part discusses "duality" in general and the second part discusses the most important duality: Hodge duality. This video has an annotation. Annotations are NOT
From playlist What is a Tensor?
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
Duality In Higher Categories IV by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
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
Lecture 11: Negative Topological cyclic homology
Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h
From playlist Topological Cyclic Homology
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 (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
Algebraic Topology - 5.3 - Mapping Spaces and the Compact Open Topology
Description of the adjunction (X \times -, Top(X,-))
From playlist Algebraic Topology
Commutative algebra 21 Tensor products and exactness
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 study when taking tensor product preserves exactness. We also show that tensor products preserve direct lim
From playlist Commutative algebra
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
Commutative algebra 23 (Flat extensions)
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 discuss flat extensions of rings. In particular we show that for flat extensions the homomorphisms of fini
From playlist Commutative algebra