Two-point tensors, or double vectors, are tensor-like quantities which transform as Euclidean vectors with respect to each of their indices. They are used in continuum mechanics to transform between reference ("material") and present ("configuration") coordinates. Examples include the deformation gradient and the first Piola–Kirchhoff stress tensor. As with many applications of tensors, Einstein summation notation is frequently used. To clarify this notation, capital indices are often used to indicate reference coordinates and lowercase for present coordinates. Thus, a two-point tensor will have one capital and one lower-case index; for example, AjM. (Wikipedia).
What is a Tensor? Lesson 11: The metric tensor
What is a Tensor 11: The Metric Tensor
From playlist What is a Tensor?
Given two points write them as a vector in component form
Learn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. Given two point vectors with one representing the initial point and the other representing the terminal point. The component form of the vector formed
From playlist Vectors
Given two points write them as a vector in component form
Learn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. Given two point vectors with one representing the initial point and the other representing the terminal point. The component form of the vector formed
From playlist Vectors
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 (3 of 28) What is a Dyad? A Graphical Representation
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the physical graphical representation of a tensor of rank 2, or a dyad. A tensor of rank 2 has 9 components, which means there will be 3 vectors each representing a force or stress or somethin
From playlist CALCULUS 3 CH 10 TENSORS
Learning to write a vector in component form given two points
Learn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. Given two point vectors with one representing the initial point and the other representing the terminal point. The component form of the vector formed
From playlist Vectors
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
Given the initial and terminal point, write the vector in component form
Learn how to write a vector in component form given two points and also how to determine the magnitude of a vector given in component form. Given two point vectors with one representing the initial point and the other representing the terminal point. The component form of the vector formed
From playlist Vectors
Nonlinear algebra, Lecture 8: "Tensors", by Bernd Sturmfels and Mateusz Michalek
This is the eight lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Ye Ke (7/29/22): Geometry of convergence analysis for low rank partially orthogonal tensor approx.
Abstract: Low rank partially orthogonal tensor approximation (LRPOTA) is an important problem in tensor computations and their applications (PCA, ICA, signal processing, data mining, latent variable model, dictionary learning, etc.). It includes Low rank orthogonal tensor approximation (LR
From playlist Applied Geometry for Data Sciences 2022
Rings 11 Tensor products of modules
This lecture is part of an online course on rings and modules. We define tensor prducts of modules over more general rings, and give some examples: coproducts of commutative rings, tensors in differential geometry, tensor products of group representations, and tensor products of fields.
From playlist Rings and modules
Anna Seigal: "Tensors in Statistics and Data Analysis"
Watch part 1/2 here: https://youtu.be/9unKtBoO5Hw Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensors in Statistics and Data Analysis" Anna Seigal - University of Oxford Abstract: I will give an overview of tensors as they arise in settings
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Joseph Landsberg: "Introduction to the Geometry of Tensors (Part 2/2)"
Watch part 1/2 here: https://youtu.be/v9lx4XN3w9c Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Introduction to the Geometry of Tensors (Part 2/2)" Joseph Landsberg - Texas A&M University - College Station, Mathematics Abstract: I will give a
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
What is General Relativity? Lesson 13 Some important CFREE relations
We prove some critical CFREE expressions required for the derivation of the metric connection. Errata: At 46:00 the argument should have the vector "Z" not the vector "X". X is part of the example tensor and Z is being fed to the tensor.
From playlist What is General Relativity?
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?
Xiao-Gang Wen: "Exactly soluble tensor network model in 2+1D with U(1) symmetry & quantize Hall ..."
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop II: Tensor Network States and Applications "Exactly soluble tensor network model in 2+1D with U(1) symmetry and quantize Hall conductance" Xiao-Gang Wen - Massachusetts Institute of Technology Abstra
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
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
Quadratic System 2 Algebra Regents
In this video we look at the intersection between and linear and quadratic function
From playlist Quadratic Systems
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)