This video explains what is meant by the Kronecker Product of two matrices, and discusses some of this operation's uses in econometrics.
Check out http://oxbridge-tutor.co.uk/graduate-econometrics-course/ for course materials, and information regarding updates on each of the courses. Check out https://ben-lambert.com/econometrics-course-problem-sets-and-data/ for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: https://ben-lambert.com/bayesian/ Accompanying this series, there will be a book: https://www.amazon.co.uk/gp/product/1473916364/ref=pe_3140701_247401851_em_1p_0_ti

Views: 18267
Ben Lambert

We can use indices to write matrix multiplication in a more compact way.

Views: 10386
PhysicsHelps

Visit http://ilectureonline.com for more math and science lectures!
In this video I will explain and visually show how tensors, scalar, vector, dyad, and triad, are represented by a matrix.
Next video in the series can be seen at:
https://youtu.be/brnzaYNFJ1w

Views: 4356
Michel van Biezen

Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors

Views: 1250560
Dan Fleisch

MATLAB
MATHEMATICS IN MATLAB
LINEAR ALGEBRA PART 2
Kronecker Tensor Product,
What is Vector Norm,
Matrix Norm,
Multi thread Computation with Linear algebra functions,
System of linear equations,
What is Mrdivide and Mldivide,
Using Multi thread Computation with system of linear equation,
Iterative methods for solving of linear equations,
Inverse and Determinants,
What is Pseudo Inverse,
Video by Edupedia World (www.edupediaworld.com), Online Education,
All Right Reserved.

Views: 2360
Edupedia World

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Views: 14054
JJtheTutor

Error: at around 13:25, on the last line, the input space should be V-tensor-(V*), not (V*)-tensor-V, although the two spaces are involve vector-covector pairs, the order is different, and so they are technically different spaces.
This one took a while to edit... kept noticing mistakes and having to go back and fix them. I'm sure there's at least

Views: 6899
eigenchris

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 6850
MathTheBeautiful

Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK

Views: 263898
Physics Videos by Eugene Khutoryansky

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Commenting and Full Lesson Available @ http://wp.me/p7kK3u-rB via WeSolveThem.com
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Description: For this lesson we are going to go over the scalar triple product in index notation, and how to prove it using the notation.
Copyright © 2013 → ∞ WeSolveThem.com - JJtheTutor, Inc. All rights reserved | Made By Students, For Students.

Views: 5794
JJtheTutor

Part 2 of lecture 1 from my representation theory lecture playlist. Topics discussed include direct sums and tensor products of vector spaces.

Views: 279
For Your Math

Tensor Product of Algebras

Views: 1972
Introduction to Commutative Algebra

Transport Phenomena tensor and vector matrix multipication operations including dot product, dyad, outer product, vector tensor dot product, double dot product.

Views: 4237
ChemE.Math

Kyle Kloster, Purdue University Math Department
PUNLAG is a student-led seminar in numerical linear algebra at Purdue University.
Definitions, examples, basic properties. In particular, how eigen-information of A \kron B is exactly determined by eigen-information of A and of B. We used a Kronecker product perspective to show an easier way of studying the Poisson matrix that caused so many students so much pain in CS515 Numerical Linear Algebra.
Continued in part 2: https://www.youtube.com/watch?v=ypN5CbB1lvY&feature=youtu.be

Views: 2808
Kyle Kloster

MIT 8.05 Quantum Physics II, Fall 2013
View the complete course: http://ocw.mit.edu/8-05F13
Instructor: Barton Zwiebach
In this lecture, the professor continued to talk about the tensor product and also talked about entangled states, Bell basis states, quantum teleportation, etc.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 8873
MIT OpenCourseWare

Homomorphisms and Tensor Products

Views: 2973
Introduction to Commutative Algebra

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"

Views: 28996
XylyXylyX

Definition of a 2nd order tensor, examples zero tensor, identity tensor, and tensor outer product with two additional examples of tensor outer product tensors.

Views: 5055
Sanjay Govindjee

Explains how invariants of linear transformations (such as trace and determinant) arise from thinking about basis-independent operations and diagrams. With corrected closed captioning.

Views: 2019
Linear Algebra

Leonid Pastur
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
April 16, 2014
We consider two classes of n×nn×n sample covariance matrices arising in quantum informatics. The first class consists of matrices whose data matrix has mm independent columns each of which is the tensor product of kk independent dd-dimensional vectors, thus n=dkn=dk. The matrices of the second class belong to n(ℂd1⊗ℂd2), n=d1d2Mn(Cd1⊗Cd2), n=d1d2 and are obtained from the standard sample covariance matrices by the partial transposition in ℂd2Cd2. We find that for the first class the limiting eigenvalue counting measure is the standard MP law despite the strong statistical dependence of the entries while for the second class the limiting eigenvalue counting measure is the shifted semicircle.
For more videos, visit http://video.ias.edu

Views: 118
Institute for Advanced Study

MIT 8.05 Quantum Physics II, Fall 2013
View the complete course: http://ocw.mit.edu/8-05F13
Instructor: Barton Zwiebach
In this lecture, the professor continued to talk about nuclear magnetic resonance and also introduced the tensor product.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 8669
MIT OpenCourseWare

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? :)

Views: 15017
XylyXylyX

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Views: 30620
JJtheTutor

Properties of Tensor Products

Views: 2203
Introduction to Commutative Algebra

MIT 8.05 Quantum Physics II, Fall 2013
View the complete course: http://ocw.mit.edu/8-05F13
Instructor: Barton Zwiebach
In this lecture, the professor talked about EPR and Bell inequalities, orbital angular momentum and central potentials, etc.
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

Views: 7710
MIT OpenCourseWare

Course web page: http://web2.slc.qc.ca/pcamire/

Views: 50484
[email protected]

In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects. In each case the significance of the symbol is the same: the freest bilinear operation. In some contexts, this product is also referred to as outer product. The general concept of a "tensor product" is captured by monoidal categories; that is, the class of all things that have a tensor product is a monoidal category. The variant of ⊗ is used in control theory.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 1805
Audiopedia

Part II of the preliminary vector stuff section of this series on Tensor Calculus. We go over transformations through rotation, space-time interval invariance, transformation coefficients as partial derivatives, vectors as Matrices (Bra-Ket Notation), outer products, completeness, calculating matrix elements, and change of basis.

Views: 2502
Andrew Dotson

Please Subscribe: https://YouTube.com/WeSolvethem
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Views: 7982
JJtheTutor

This course will continue on Patreon at http://bit.ly/PavelPatreon
Textbook: http://bit.ly/ITCYTNew
Solutions: http://bit.ly/ITACMS_Sol_Set_YT Errata: http://bit.ly/ITAErrata
McConnell's classic: http://bit.ly/MCTensors
Weyl's masterpiece: http://bit.ly/SpaceTimeMatter Levi-Civita's classic: http://bit.ly/LCTensors Linear Algebra Videos: http://bit.ly/LAonYT
Table of Contents of http://bit.ly/ITCYTNew
Rules of the Game
Coordinate Systems and the Role of Tensor Calculus
Change of Coordinates
The Tensor Description of Euclidean Spaces
The Tensor Property
Elements of Linear Algebra in Tensor Notation
Covariant Differentiation
Determinants and the Levi-Civita Symbol
The Tensor Description of Embedded Surfaces
The Covariant Surface Derivative
Curvature
Embedded Curves
Integration and Gauss’s Theorem
The Foundations of the Calculus of Moving Surfaces
Extension to Arbitrary Tensors
Applications of the Calculus of Moving Surfaces
Index:
Absolute tensor
Affine coordinates
Arc length
Beltrami operator
Bianchi identities
Binormal of a curve
Cartesian coordinates
Christoffel symbol
Codazzi equation
Contraction theorem
Contravaraint metric tensor
Contravariant basis
Contravariant components
Contravariant metric tensor
Coordinate basis
Covariant basis
Covariant derivative
Metrinilic property
Covariant metric tensor
Covariant tensor
Curl
Curvature normal
Curvature tensor
Cuvature of a curve
Cylindrical axis
Cylindrical coordinates
Delta systems
Differentiation of vector fields
Directional derivative
Dirichlet boundary condition
Divergence
Divergence theorem
Dummy index
Einstein summation convention
Einstein tensor
Equation of a geodesic
Euclidean space
Extrinsic curvature tensor
First groundform
Fluid film equations
Frenet formulas
Gauss’s theorem
Gauss’s Theorema Egregium
Gauss–Bonnet theorem
Gauss–Codazzi equation
Gaussian curvature
Genus of a closed surface
Geodesic
Gradient
Index juggling
Inner product matrix
Intrinsic derivative
Invariant
Invariant time derivative
Jolt of a particle
Kronecker symbol
Levi-Civita symbol
Mean curvature
Metric tensor
Metrics
Minimal surface
Normal derivative
Normal velocity
Orientation of a coordinate system
Orientation preserving coordinate change
Relative invariant
Relative tensor
Repeated index
Ricci tensor
Riemann space
Riemann–Christoffel tensor
Scalar
Scalar curvature
Second groundform
Shift tensor
Stokes’ theorem
Surface divergence
Surface Laplacian
Surge of a particle
Tangential coordinate velocity
Tensor property
Theorema Egregium
Third groundform
Thomas formula
Time evolution of integrals
Torsion of a curve
Total curvature
Variant
Vector
Parallelism along a curve
Permutation symbol
Polar coordinates
Position vector
Principal curvatures
Principal normal
Quotient theorem
Radius vector
Rayleigh quotient
Rectilinear coordinates
Vector curvature normal
Vector curvature tensor
Velocity of an interface
Volume element
Voss–Weyl formula
Weingarten’s formula
Applications: Differenital Geometry, Relativity

Views: 21392
MathTheBeautiful

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 the series can be seen at:
https://youtu.be/ir-Eg684MR4

Views: 8494
Michel van Biezen

Overview of Chapter 10, Tensor Products, in "A Course in Quantum Computing" (by Michael Loceff)

Views: 3470
michael loceff

In this tutorial we discuss TensorFlow basics and we take a deep dive into tesnors and tensor operations. In the math behind it, we discuss standard deviation, variance and dot product of matrices.
Github:
https://github.com/TwistedHardware/mltutorial/blob/master/notebooks/tf/2.%20Tensors.ipynb
Twitter:
https://twitter.com/twistedhardware
T-Shirt:
https://teespring.com/stores/roshan

Views: 429
Roshan

The National MagLab hed it's fifth Theory Winter School in Tallahassee, FL from January 9th - 13th, 2017. This year's focus was on modeling of correlated electron materials, an area that received much interest in recent years, with the long-term goal leading to the predictive design of new high-temperature superconductors and other functional quantum materials.

Views: 342
National MagLab

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Views: 15352
JJtheTutor

Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown

Views: 907832
3Blue1Brown

My tensor series is finally here! In this video, I introduce the concept of tensors. I begin by talking about scalars, then vectors, then rank-2 tensors (whose explanation takes up the bulk of the video since these are probably the most difficult to understand out of the three).
I then move on to define tensors (without specifying their transformation properties), after which I conclude the video with a short discussion on rank-3 tensors, which may be represented by 3-D matrices/arrays.
Questions/requests? Let me know in the comments!
Pre-requisites: You basically need to know what vectors, scalars, and matrices are. Nothing much more to it. A 1st-year Physics + Linear Algebra course should be enough.
Lecture Notes: https://drive.google.com/open?id=1O5GOXA-oJsrn3j8ZHnk-CecPEA79uiJv
Patreon: https://www.patreon.com/user?u=4354534
Twitter: https://twitter.com/FacultyOfKhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
- Jose Lockhart
- Yuan Gao
- James Mark Wilson
- Marcin Maciejewski
- Sabre
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques

Views: 19144
Faculty of Khan