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The Kronecker Product of two matrices - an introduction
 
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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
Matrix multiplication with tensor notation
 
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We can use indices to write matrix multiplication in a more compact way.
Views: 11244 PhysicsHelps
Tensor products
 
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I discuss tensor products.
Views: 58159 Jim Fowler
Introduction to Tensors
 
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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
Calculus 3: Tensors (2 of 28) Tensors Represented in a Matrix
 
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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
44 - The Kronecker Product of two matrices - an introduction
 
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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
What's a Tensor?
 
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Dan Fleisch briefly explains some vector and tensor concepts from A Student's Guide to Vectors and Tensors
Views: 1423700 Dan Fleisch
Tensor product
 
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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
Inner & outer products
 
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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
19 Linear Algebra in Matlab Part 2 Kronecker Tensor Product | Matrix Norm | Multi Thread Computation
 
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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
Tensor Operations: Contractions, Inner Products, Outer Products
 
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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
Tensors for Beginners 15: Tensor Product Spaces
 
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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
Index/Tensor Notation: The Scalar Triple Product - Lesson 12
 
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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
 
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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
Tensor Algebra
 
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Overview of Chapter 10, Tensor Products, in "A Course in Quantum Computing" (by Michael Loceff)
Views: 3939 michael loceff
Machine Learning Maths | Matrix Operations | Transpose | Tensors | Part 1 | Eduonix
 
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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 Follow Eduonix on other social networks: ■ Facebook: https://goo.gl/ZqRVjS ■ Twitter: https://goo.gl/oRDaji ■ Google+: https://goo.gl/mfPaxx ■ Instagram: https://goo.gl/7f5DUC | @eduonix ■ Linkedin: https://goo.gl/9LLmmJ ■ Pinterest: https://goo.gl/PczPjp
What is a Tensor 5: Tensor Products
 
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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
19. Multiparticle States and Tensor Products (continued)
 
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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
Garnet Chan "Matrix product states, DMRG, and tensor networks" (Part 1 of 2)
 
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Garnet Chan Matrix product states, DMRG, and tensor networks Part 1 of 2 Day 4, Session 2 Summer School on Emergent Phenomena in Quantum Materials 2015 @ Cornell http://www.lassp.cornell.edu/events/epiqs2015
Lecture 14 - Homomorphisms and Tensor Products
 
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Homomorphisms and Tensor Products
Calculus 3: Tensors (3 of 28) What is a Dyad? A Graphical Representation
 
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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
General Inner Products in ℝⁿ. Matrix Representation
 
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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
Lecture 17 - Tensor Product of Algebras
 
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Tensor Product of Algebras
What is a Tensor 6: Tensor Product Spaces
 
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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
Norbert Schuch: Matrix product states and tensor networks (I)
 
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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
Basic Tensors and the Tensor Outer Product - rev
 
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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
Limiting Eigenvalue Distribution of Random Matrices Involving Tensor Product - Leonid Pastur
 
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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
18. Two State Systems (continued), Multiparticle States and Tensor Products
 
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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
Trace and determinant as invariants, tensor product, diagrams
 
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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
Mod-01 Lec-03 Vectors and Tensors
 
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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
The Kronecker Product 1 - Kyle Kloster
 
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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
Tensor Calculus 3: The Jacobian
 
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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
Index/Tensor Notation: The scalar or dot product - Lesson 2
 
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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
Vector and Tensor Notation
 
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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 Explained Intuitively: Covariant, Contravariant, Rank
 
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Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK
Tensor Calculus For Physics Majors 002 | Vector Transformations and Vectors as Matrices
 
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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
Outer Product
 
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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
Quantum Theory, Lecture 10: Entanglement. Tensor Products. Measurement.
 
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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
Tensor Calculus Lecture 12b: Inner Products in Tensor Notation
 
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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
Kronecker Matrix Product - properties
 
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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

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