Multilinear algebra | Tensors | Differential geometry | Differential topology
In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences. As a tensor is a generalization of a scalar (a pure number representing a value, for example speed) and a vector (a pure number plus a direction, like velocity), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space. Many mathematical structures called "tensors" are tensor fields. For example, the Riemann curvature tensor is not a tensor, as the name implies, but a tensor field: it is named after Bernhard Riemann, and associates a tensor to each point of a Riemannian manifold, which is a topological space. (Wikipedia).
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?
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 16: The metric tensor field
What is a Tensor? Lesson 16: The metric tensor field
From playlist What is a Tensor?
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?
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
What is a Tensor 10: Metric spaces
What is a Tensor 10: Metric spaces
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What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
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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
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?
An Introduction to Tensor Renormalization Group (Lecture 2) by Daisuke Kadoh
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
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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
Lecture 7 | Quantum Entanglements, Part 3 (Stanford)
Lecture 7 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 3, Spring 2007). Recorded May 21, 2007 at Stanford University. This Stanford Continuing Studies course is the third of a three-quarter sequence of classes exploring the "quantum entanglements" in modern
From playlist Lecture Collection | Quantum Entanglements: Part 3 (Spring 2007)
Tensor Network Methods in Four Dimensional Field Theory by Daisuke Kadoh
PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)
The Einstein Field Equations | Tensor Calc Finale
Today we use all the tools we've got in our back pocket to "derive" the Einstein Field Equations of general relativity. It's more of a motivation than a derivation, I suppose. This series is based off the book "Tensor Calculus for Physics" by Dwight Neuenschwander: https://amzn.to/3rEema3
From playlist New To Tensors? Start Here
An Introduction to Tensor Renormalization Group by Daisuke Kadoh
PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II
From playlist NUMSTRING 2022
What is General Relativity? Lesson 39: The curvature - formal introduction
What is General Relativity? Lesson 39: The curvature - formal introduction The Riemann Curvature Tensor is presented as a strictly formal object. Take note of an error captured by viewer "Endevor" in the comments. I may redo this video soon to fix it! Please consider supporting this chan
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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.
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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?