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Matrix multiplication with tensor notation
 
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We can use indices to write matrix multiplication in a more compact way.
Views: 11405 PhysicsHelps
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: 23235 Ben Lambert
Tensor products
 
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I discuss tensor products.
Views: 59048 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: 50685 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: 8523 Michel van Biezen
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: 9903 MIT OpenCourseWare
Tensors/tensor products demystified
 
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Help me keep making videos: http://paypal.me/mlbakermath I'm baaaaack! ;-) Achieving a full understanding of the formalism of tensors is one thing that COMPLETELY transformed my view of linear algebra; thereafter every concept in differential geometry, representation theory, etc. seemed absolutely natural. I want to share this elegant, unified viewpoint with you (*cough* and people are always badgering me to repost rather embarrassing videos I recorded on the topic as a young and naive undergrad, which I REFUSE to do, so there). Now I just need to make some videos on geometric algebra/calculus... then things will get really fun.
Views: 21064 mlbaker
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: 5525 Sanjay Govindjee
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: 32448 XylyXylyX
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: 1460379 Dan Fleisch
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! Learn It Up! Summer’s Hottest Learning Sale Is Here! Pick Any Sun-sational Course & Get Other Absolutely FREE! Link: http://bit.ly/summer-bogo-2019 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
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
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: 12372 eigenchris
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: 976 Ox educ
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: 10512 MIT OpenCourseWare
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
Multiplication of Tensor || Product of Tensor
 
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Multiplication of Tensor. Product of Tensor. Multiplication of two Tensor. Product of two Tensor. Multiplication of two Tensor with examples. Donate - Google Pay - 8265971820 #MultiplicationOfTensor #ProductOfTensor Like share subscribe Please check Playlist for more. Thanks for watching #mathematicsAnalysis
Lecture 14 - Homomorphisms and Tensor Products
 
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Homomorphisms and Tensor Products
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: 2704 Edupedia World
Lecture 17 - Tensor Product of Algebras
 
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Tensor Product of Algebras
Powers of Tensors and Fast Matrix Multiplication
 
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Francois Le Gall, University of Tokyo Tensors in Computer Science and Geometry http://simons.berkeley.edu/talks/francois-le-gall-2014-11-12
Views: 842 Simons Institute
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: 2275 Linear Algebra
Tensor Algebra
 
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Overview of Chapter 10, Tensor Products, in "A Course in Quantum Computing" (by Michael Loceff)
Views: 4030 michael loceff
The Trace of a Square Matrix
 
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Course web page: http://web2.slc.qc.ca/pcamire/
Views: 54507 [email protected]
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
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
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: 4881 ChemE.Math
Norbert Schuch: Matrix product states and tensor networks (II)
 
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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: 365 Microsoft Research
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: 1981 Audiopedia
VIDEO II - VECTOR AND TENSOR  - DOT PRODUCT AND APPLICATIONS
 
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This video deals with the definition of the dot product under the geometric viewpoint. The standard basis are also used to determine the dot product of two vectors.
Views: 1247 Carlos Thompson
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: 8820 MIT OpenCourseWare
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: 432 For Your Math
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: 13069 eigenchris
Norbert Schuch: Matrix product states and tensor networks (I)
 
01:04:53
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: 1160 Microsoft Research
Linear Algebra 20L: The Dot Product in Non-Cartesian Bases, the Gram Matrix or the Metric
 
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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: 5449 MathTheBeautiful
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: 7548 Andrew Dotson
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: 486 National MagLab
Garnet Chan "Matrix product states, DMRG, and tensor networks" (Part 2 of 2)
 
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Garnet Chan Matrix product states, DMRG, and tensor networks Part 2 of 2 Day 4, Session 3 Summer School on Emergent Phenomena in Quantum Materials 2015 @ Cornell http://www.lassp.cornell.edu/events/epiqs2015
22 Quantum Mechanics - Two qubit gates and tensor products
 
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Two qubit gates and tensor products
Views: 2539 intrigano
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: 3844 Alexander Maloney