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: 22526
Ben Lambert

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

Views: 11244
PhysicsHelps

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: 45112
Faculty of Khan

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: 7883
Michel van Biezen

This video explains what is meant by the Kronecker Product of two matrices, and discusses some of this operation's uses in econometrics.
If you are interested in seeing more of the material on graduate level econometrics, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXj-nXiNzO1aaItNDm30e01 For more information on econometrics and Bayesian statistics, see: https://ben-lambert.com/

Views: 957
Ox educ

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

Views: 1423700
Dan Fleisch

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: 1959
Audiopedia

Definition of an inner and outer product of two column vectors.
Take my Coursera course at
https://www.coursera.org/learn/matrix-algebra-engineers
Download lecture notes from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Views: 3353
Jeffrey Chasnov

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: 2668
Edupedia World

In this video, I continue the discussion on tensor operations by defining the contraction, inner product, and outer product. I provide some short examples of each of these operations, which will hopefully solidify your understanding of how these operations work.
Questions/requests? Let me know in the comments!
Pre-reqs: The previous videos in the playlist - https://www.youtube.com/playlist?list=PLdgVBOaXkb9D6zw47gsrtE5XqLeRPh27_
Lecture Notes: https://drive.google.com/open?id=1PUSPfoI7g8lcU0-Gzcxi9n9pBdMXjjKY
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:
- Anonymous
- Cesar Garza
- Odissei
- Alvin Barnabas
- Jacob Soares
- Yenyo Pal
- Lisa Bouchard
- Bernardo Marques
- Connor Mooneyhan
- Richard McNair
- Guillaume Chereau
- Patapom
- Vitor Ciaramella
- McKay Oyler
- Dieter Walter Reule
EDIT: At 8:35, when I write the components of a, I meant to use superscripts instead of subscripts! a is a contravariant tensor, so superscripts are the way to go!

Views: 1121
Faculty of Khan

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: 11384
eigenchris

Leave a tip for good service: https://paypal.me/jjthetutor
Student Solution Manuals: https://amzn.to/2WZrFnD
More help via http://jjthetutor.com
Download my eBooks via http://payhip.com/jjthetutor,
paperback via http://amazon.com/author/jjthetutor.

Views: 8240
JJtheTutor

Tensor product (Tensor Algebra)
Tensor product of the type (r+r', s+s')
#tensorProduct #tensorCalculas
Donate -
Google Pay - 8265971820
Like share subscribe.
Please check Playlist for more vedios.
Thanks for watching #mathematicsAnalysis

Views: 551
Mathematics Analysis

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

Views: 3939
michael loceff

Math is an essential part of Machine Learning. It involves various activities like selecting the perfect algorithm, choosing different parameters, estimating intervals and uncertainty. And math plays a very crucial role in all of these activities.
This series will help you cover all the mathematical knowledge you will need to practice Machine Learning.
In our first part, we will be talking about different topics namely:
1. The basics - Scalars and Vectors
2. Matrix Operations
3. Tensors
4. Matrix Transpose
Are you excited to learn about all this? Let's begin!
Want to learn Machine learning in detail? Then try our course Mathematical Foundation For Machine Learning and AI. Apply coupon code "YOUTUBE10" to get this course for $10
http://bit.ly/2Mi5IuP
Kickstarter Campaign on AI and ML E-Degree is Launched. Back this Campaign and Explore all the Courses with over 58 Hours of Learning.
Link- http://bit.ly/aimledegree
Thank you for watching! We’d love to know your thoughts in the comments section below. Also, don’t forget to hit the ‘like’ button and ‘subscribe’ to ‘Eduonix Learning Solutions’ for regular updates. https://goo.gl/BCmVLG
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Views: 4781
Eduonix Learning Solutions

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: 31884
XylyXylyX

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: 10312
MIT OpenCourseWare

Homomorphisms and Tensor Products

Views: 3840
Introduction to Commutative Algebra

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 something requiring x-, y-, z- representation.
Next video in the series can be seen at:
https://youtu.be/1AEeiLjUf1o

Views: 8257
Michel van Biezen

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: 9236
MathTheBeautiful

Tensor Product of Algebras

Views: 2406
Introduction to Commutative Algebra

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: 16614
XylyXylyX

Interacting systems of many quantum particles exhibit rich physics due to their underlying entanglement, and are a topic of major interest in several areas of physics. In recent years, quantum information ideas have allowed us to understand the entanglement structure of such systems, and to come up with novel ways to describe and study them. In my lecture, I will first explain how we can describe such systems based on their entanglement structure, giving rise to so-called Tensor Network States. I will then discuss how these concepts can be used to model strongly interacting many-body systems and to study the different exotic topological states of matter based on their entanglement, and I will briefly highlight their suitability for numerical simulations. Finally, I will discuss open mathematical and physical challenges in the field.

Views: 1141
Microsoft Research

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: 5472
Sanjay Govindjee

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: 145
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: 9733
MIT OpenCourseWare

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: 2214
Linear Algebra

Fundamentals of Transport Processes - II by Prof. V. Kumaran,Department of Chemical Engineering,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in

Views: 68446
nptelhrd

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: 3108
Kyle Kloster

Forward and Backward Transforms first video: https://www.youtube.com/watch?v=sdCmW5N1LW4
MINOR ERROR: I sometimes write the cartesian and polar variables ("c" and "p") with superscript indexes, and sometimes with subscript indexes. This is my mistake. In general they should always be written with superscripts.
Reuploaded to fix some errors.

Views: 11920
eigenchris

Leave a tip for good service: https://paypal.me/jjthetutor
Student Solution Manuals: https://amzn.to/2WZrFnD
More help via http://jjthetutor.com
Download my eBooks via http://payhip.com/jjthetutor,
paperback via http://amazon.com/author/jjthetutor.

Views: 18476
JJtheTutor

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

Views: 4820
ChemE.Math

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

Views: 344503
Physics Videos by Eugene Khutoryansky

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: 6165
Andrew Dotson

What does a matrix with rank 1 look like? Watch this video and find out! Featuring the outer product, a close companion to the dot product
Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0
Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw

Views: 1441
Dr Peyam

Lecture 10 of my Quantum Theory course at McGill University, Fall 2012. Entanglement. Tensor Products. Measurement.
The course webpage, including links to other lectures and problem sets, is available at
http://www.physics.mcgill.ca/~maloney/551/
The written notes for this lecture are available at
http://www.physics.mcgill.ca/~maloney/551/551-10.pdf

Views: 3794
Alexander Maloney

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: 5040
MathTheBeautiful

This video provides a description of the properties of the Kronecker matrix Product, which then allow for construction of more elaborate estimators in matrix form.
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: 6601
Ben Lambert