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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: 18267 Ben Lambert
Tensor products
 
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I discuss tensor products.
Views: 53249 Jim Fowler
Matrix multiplication with tensor notation
 
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We can use indices to write matrix multiplication in a more compact way.
Views: 10386 PhysicsHelps
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: 4356 Michel van Biezen
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: 1250560 Dan Fleisch
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: 2360 Edupedia World
Index/Tensor Notation: The scalar or dot product - Lesson 2
 
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Please Subscribe: https://YouTube.com/WeSolveThem Tip for Good Service: https://PayPal.me/WeSolveThem Thousands of free solutions: https://WeSolveThem.com
Views: 14054 JJtheTutor
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: 6899 eigenchris
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: 6850 MathTheBeautiful
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
Index/Tensor Notation: The Scalar Triple Product - Lesson 12
 
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Subscribe for More Lessons: https://YouTube.com/WeSolveThem Tip for Good Service: https://PayPal.me/WeSolveThem Thousands of free solutions: https://WeSolveThem.com Commenting and Full Lesson Available @ http://wp.me/p7kK3u-rB via WeSolveThem.com Lessons are always AD-FREE @ WeSolveThem.com 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
Representation Lecture 1.2: Direct Sums and Tensor Products
 
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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
Lecture 17 - Tensor Product of Algebras
 
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Tensor Product of Algebras
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: 4237 ChemE.Math
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: 2808 Kyle Kloster
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: 8873 MIT OpenCourseWare
Lecture 14 - Homomorphisms and Tensor Products
 
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Homomorphisms and Tensor Products
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: 28996 XylyXylyX
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: 5055 Sanjay Govindjee
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: 2019 Linear Algebra
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: 8669 MIT OpenCourseWare
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: 15017 XylyXylyX
Index/Tensor Notation - Introduction to The Kronecker Delta - Lesson 1
 
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Subscribe for More Lessons: https://YouTube.com/WeSolveThem Tip for Good Service: https://PayPal.me/WeSolveThem Thousands of free solutions: https://WeSolveThem.com All lessons are available AD-FREE when you sign up via http://indexnotation.com/register
Views: 30620 JJtheTutor
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 15 - Properties of Tensor Products
 
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Properties of Tensor Products
20. Multiparticle States and Tensor Products (continued) and Angular Momentum
 
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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 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
The Trace of a Square Matrix
 
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Course web page: http://web2.slc.qc.ca/pcamire/
Views: 50484 [email protected]
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: 1805 Audiopedia
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: 2502 Andrew Dotson
Index/Tensor Notation: Permutations and The Determinant - Lesson 10
 
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Views: 7982 JJtheTutor
Tensor Calculus 4e: Decomposition by Dot Product 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: 21392 MathTheBeautiful
Calculus 3: Tensors (1 of 28) What is a Tensor?
 
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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
Tensor Algebra
 
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Overview of Chapter 10, Tensor Products, in "A Course in Quantum Computing" (by Michael Loceff)
Views: 3470 michael loceff
TensorFlow - Tensors #2
 
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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
MagLab Theory Winter School 2017: Ulrich Schollwock - DMRG & Tensor Product State (TPS) Methods
 
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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
Index/Tensor Notation: Reducing The Kronecker Delta - Lesson 3
 
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Please Subscribe: https://YouTube.com/WeSolveThem Tip for Good Service: https://PayPal.me/WeSolveThem Thousands of free solutions: https://WeSolveThem.com
Views: 15352 JJtheTutor
Linear transformations and matrices | Essence of linear algebra, chapter 3
 
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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
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: 19144 Faculty of Khan

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