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Gernot Akemann Universität Bielefeld March 19, 2014 For more videos, visit http://video.ias.edu
Speaker: P. Vivo (King's College, London) Spring College on the Physics of Complex Systems | (smr 3113) 2017_04_11-09_00-smr3113
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
This video explains what is meant by the expectations and variance of a vector of random variables. 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: 28179 Ben Lambert
The direct product is a way to combine two groups into a new, larger group. Just as you can factor integers into prime numbers, you can break apart some groups into a direct product of simpler groups. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 61185 Socratica
Yan Fyodorov Queen Mary University of London October 3, 2013 I will start with discussing the relation between a class of disorder-generated multifractals and logarithmically-correlated random fields and processes. An important example of the latter is provided by the so-called "1/f noise" which, in particular, emerges naturally in studies of characteristic polynomials of CUE matrices. Extending the consideration to GUE setting reveals more processes of that type, in particular a special singular limit of the Fractional Brownian Motion. In the rest of the talk I will attempt to show how to use heuristic insights from Statistical Mechanics of disordered systems to arrive to detailed conjectures about distributions of high and extreme values of logarithmically correlated processes and multifractals, including the absolute maximum of the Riemann zeta-function in intervals of the critical line. For more videos, visit http://video.ias.edu
Thanks to all of you who support me on Patreon. You da real mvps! \$1 per month helps!! :) https://www.patreon.com/patrickjmt !! Graph Theory - An Introduction! In this video, I discuss some basic terminology and ideas for a graph: vertex set, edge set, cardinality, degree of a vertex, isomorphic graphs, adjacency lists, adjacency matrix, trees and circuits. There is a MISTAKE on the adjacency matrix; I put a 1 in the v5 row and v5 column, but it should be placed in the v5 row and the v6 column. There are annotations pointing this out along with the corrected matrix!
Views: 442453 patrickJMT
The free probability perspective on random matrices is that the large size limit of random matrices is given by some (usually interesting) operators on Hilbert spaces and corresponding operator algebras. The prototypical example for this is that independent GUE random matrices converge to free semicircular operators, which generate the free group von Neumann algebra. The usual convergence in distribution has been strengthened in recent years to a strong convergence, also taking operator norms into account. All this is on the level of polynomials. In my talk I will recall this and then go over from polynomials to rational functions (in non-commuting variables). Unbounded operators will also play a role. Research problem presented at the 27th Annual PCMI Summer Session, Random Matrices, held June 25 – July 15, 2017. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI). The Institute for Advanced Study / IAS / Park City Mathematics Institute (PCMI) is designed for mathematics educators at the secondary and post-secondary level, as well as mathematics researchers and students at the post-secondary level. These groups find at PCMI an intensive mathematical experience geared to their individual needs. Moreover, the interaction among groups with different backgrounds and professional needs increases each participant’s appreciation of the mathematical community as a whole as well as the work of participants in different areas. For more information, visit https://pcmi.ias.edu
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be promptly addressed. Linear Algebra is one of the most important subjects in mathematics. It is a subject with boundless practical and conceptual applications. Linear Algebra is the fabric by which the worlds of geometry and algebra are united at the most profound level and through which these two mathematical worlds make each other far more powerful than they ever were individually. Virtually all subsequent subjects, including applied mathematics, physics, and all forms of engineering, are deeply rooted in Linear Algebra and cannot be understood without a thorough understanding of Linear Algebra. Linear Algebra provides the framework and the language for expressing the most fundamental relationships in virtually all subjects. This collection of videos is meant as a stand along self-contained course. There are no prerequisites. Our focus is on depth, understanding and applications. Our innovative approach emphasizes the geometric and algorithmic perspective and was designed to be fun and accessible for learners of all levels. Numerous exercises will be provided via the Lemma system (under development) We will cover the following topics: Vectors Linear combinations Decomposition Linear independence Null space Span Linear systems Gaussian elimination Matrix multiplication and matrix algebra The inverse of a matrix Elementary matrices LU decomposition LDU decomposition Linear transformations Determinants Cofactors Eigenvalues Eigenvectors Eigenvalue decomposition (also known as the spectral decomposition) Inner product (also known as the scalar product and dot product) Self-adjoint matrices Symmetric matrices Positive definite matrices Cholesky decomposition Gram-Schmidt orthogonalization QR decomposition Elements of numerical linear algebra I’m Pavel Grinfeld. I’m an applied mathematician. I study problems in differential geometry, particularly with moving surfaces.
Views: 1641 MathTheBeautiful
This video provides an introduction as to how we can derive the variance-covariance matrix for a set of indicator variables, when we use the matrix notation form of factor analysis models. 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: 78151 Ben Lambert
This video explains what is meant by the covariance and correlation between two random variables, providing some intuition for their respective mathematical formulations. 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: 285494 Ben Lambert
A lesson on the Hadamard matrix
Views: 13678 Jason Yao
MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Srinivas Devadas In this lecture, Professor Devadas introduces randomized algorithms, looking at solving sorting problems with this new tool. License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 21380 MIT OpenCourseWare
by Euler product for Hilbert Polya conjecture
Views: 59 enlong chiou
This video shows you how to do matrix calculation such as Matrix Determinant, matrix inverse, matrix addition, matrix multiplication, transposition and more. Quick starter guide: http://bit.ly/2WDxx5z Tutorial by Equaser I need your help. I appreciate it. Please visit my other channel and subscribe. http://bit.ly/2tGgYc4 20180325-AD
Views: 65048 Equaser.com
Jelani Nelson Member, School of Mathematics, Institute for Advanced Study March 11, 2013 fundamental theorem in linear algebra is that any real n x d matrix has a singular value decomposition (SVD). Several important numerical linear algebra problems can be solved efficiently once the SVD of an input matrix is computed: e.g. least squares regression, low rank approximation, and computing preconditioners, just to name a few. Unfortunately in many modern big data applications the input matrix is very large, so that computing the SVD is computationally expensive. Following a line of work of [Sarlós, 2006] and [Clarkson and Woodruff, 2013] on using dimensionality reduction techniques for solving numerical linear algebra problems, we show that several such problems with input matrices of size n x d can be automatically transformed into a new instance of the problem that has size very close to d x d, and thus can be solved much more quickly. Furthermore, executing these transformations require time only linear, or nearly linear, in the number of non-zero entries in the input matrix. Our techniques are of independent interest in random matrix theory, and the main technical contribution of our work turns out to be an analysis of the smallest and largest eigenvalues of certain random matrices. This talk is based on joint work with Huy Lê Nguyen (Princeton). For more videos, visit http://video.ias.edu
Benoît Collins's talk from the "Noncommutative L^p Spaces, Operator Spaces, and Applications" workshop held at Banff in June of 2010. The conference website, where the videos can be downloaded, can be found here: http://www.birs.ca/events/2010/5-day-workshops/10w5005/videos
Views: 329 LeonhardEuler1
This video shows you how to use np.random.random(()) to create random arrays of size n with entries between any numbers you desire. This is a Python anaconda tutorial for help with coding, programming, or computer science. These are short python videos dedicated to troubleshooting python problems and learning Python syntax. For more videos see Python Help playlist by Rylan Fowers. ✅Subscribe: https://www.youtube.com/channel/UCub4qT8Sgm7ytZsO-jLL4Ow?sub_confirmation=1 📺Channel: https://www.youtube.com/channel/UCub4qT8Sgm7ytZsO-jLL4Ow? ▶️Watch Latest Python Content: https://www.youtube.com/watch?v=myCPgAO9BgQ&list=PLL3Qv26_SCsGWTF5PRaWUY0yhURFvco7L ▶️Watch Latest Other Content: https://www.youtube.com/watch?v=2YfQsLd2Ups&list=PLL3Qv26_SCsFVXXdsxOSB00RSByLSJICj&index=1 🐦Follow Rylan on Twitter: https://twitter.com/rylanpfowers The creator studies Applied and Computational Mathematics at BYU (BYU ACME or BYU Applied Math) and does work for the BYU Chemical Engineering Department RANDOM ARRAY In this video let me show you some examples of how to create random matrices in python. We import numpy as np and random First just type np.random.ranom and then enter a tuple with the size of the disred random matrix. It will automatically create a matrix with entries between 1 and 0 If we want to change the value range, we can multiply by twice the value desired and then subtract the value desired from the end So if we want entries between -5 and 5 we multiply by 10 and minus 5. So if you think about it this way, the max number it could be is 10 - 5 = 5 and the min number it could be is 0 - 5 = -5 So if we want entries between -100 and 100 we multiply by 200 and minus 100. So if you think about it this way, the max number it could be is 200 - 100 = 100 and the min number it could be is 0 - 100 = -100 There you have it, that is how you create random arrays in python
Views: 666 Rylan Fowers
Multiplying two 2x2 matrices. Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/multiplying_a_matrix_by_a_matrix?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription
Views: 1108472 Khan Academy
Balint Virag Univ Toronto April 1, 2014 For more videos, visit http://video.ias.edu
Theoretical analysis of Spectral Clustering is often based on the theory of random matrices which assumes that all entries of the data matrix (with each row representing a data object) are independent random variables. In practice, however, while the objects may be independent of each other, features of an object are not independent. To address this, we will prove bounds on the singular values of a matrix assuming only that its rows are independent vector-valued random variables (the columns may not be independent) and describe a new clustering algorithm with this limited independence. In the second part, we address a more theoretical question. We will show a generalization of Azuma's (martingale) inequality to the case when the random variables are matrices and more generally infinite-dimensional operators. The first part is joint work with A. Dasgupta, J. Hopcroft and P. Mitra.
Views: 202 Microsoft Research
This instructional video demonstrates the uses of MINVERSE and MMULT functions of Microsoft Excel to find the product and inverse of matrices. It is developed for my operations research classes. Note: The videos on this channel are instructional videos developed for the classes that I teach at the department of Industrial Engineering, Morgan State University in Baltimore Maryland.
Views: 2368 DrSalimian
This talk was given on Friday, November 17, at the CDM conference at Harvard University
Views: 1232 Harvard Math
Views: 1133126 Khan Academy
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: 1104 Microsoft Research
Razvan Gurau / 23.10.17 Invitation to Random Tensors Random matrices are ubiquitous in modern theoretical physics and provide insights on a wealth of phenomena, from the spectra of heavy nuclei to the theory of strong interactions or random two dimensional surfaces. The backbone of all the analytical results in matrix models is their 1/N expansion (where N is the size of the matrix). Despite early attempts in the '90, the generalization of this 1/N expansion to higher dimensional random tensor models has proven very challenging. This changed with the discovery of the 1/N expansion (originally for colored and subsequently for arbitrary invariant) tensor models in 2010. I this talk I will present a short introduction to the modern theory of random tensors and its connections to conformal field theory and random higher dimensional geometry. ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com/InHenriPoincare Instagram : https://www.instagram.com/instituthenripoincare/ LinkedIn : https://www.linkedin.com/company-beta/11054846/
Speaker: Horng-Tzer Yau (Harvard University, USA)
Views: 629 NCTS Math Division
Markov Matrices Instructor: David Shirokoff View the complete course: http://ocw.mit.edu/18-06SCF11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Views: 97892 MIT OpenCourseWare
Title: Limit theorems for eigenvectors of the normalized Laplacian for random graphs by Minh Hai Tang from Johns Hopkins University Abstract: "We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized Laplacian converge to multivariate normals and furthermore the mean and the covariance matrix of each row are functions of the associated vertex's block membership. Together with prior results for the eigenvectors of the adjacency matrix, we then compare, via the Chernoff information between multivariate normal distributions, how the choice of embedding method impacts subsequent inference. We demonstrate that neither embedding method dominates with respect to the inference task of recovering the latent block assignments.”
Views: 15780 Simple Snippets
In this video, you will learn the fundamental concept of matrix multiplication from scratch. You can find the code in the Github link below: https://github.com/mohendra/My_Projects/tree/master/python
Views: 4910 AI Medicines
Van Vu Rutgers University June 17, 2010 For more videos, visit http://video.ias.edu
Properties of the multivariate Gaussian probability distribution
Views: 98318 Alexander Ihler
This video explains what is meant by the expectations and variance of a vector of random variables. 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: 19137 Ben Lambert
Rafal Latała, Uniwersytet Warszawski Norms of random matrices with independent entries The spectral norm of any matrix is bigger than the largest Euclidean norm of its rows and columns. We show that for Gaussian matrices with independent entries this obvious bound may be reversed in average up to a universal constant. We will also discuss similar bounds for Schatten norms and other random matrices with independent entries. The talk is based on a joint work with Ramon van Handel (Princeton) and Pierre Youssef (Paris).
Project Name: Mathematical sciences without walls Project Investigator: Dr. R. Ramanujam Module Name: Limited theorems for Spectral Statistics of Large Random Matrices by Leonid Pastur
Views: 28 Vidya-mitra
''' Matrices and Vector with Python Session # 1 Topic to be covered - 1. How to create Matrices 2. How to create random matrices of different orders 3. How to access the matrices elements 4. How to delete rows and column of a matrix. ''' ''' Q) What is Matrix? Matrix is a rectangular array of numbers, symbols or expression arranged in rows and columsn. Q) Where do we use matrix in Machine Learning? Matrix are used to read the input data which is in the form of .csv, .txt, .xml and other formats. It is especially used to processed as the input data varible (X) when training the algorithm. ''' import numpy as np #1. How to create Matrices matrix = np.array([[3,4], [5,8]]) # How to create using random #2. How to create random matrices of different orders #import random print(np.random.random((2,2))) print(np.random.random((3,3))) print(np.random.random_integers(0,9,(2,2))) print(np.random.randint(0,100,(5,5))) # 3. How to access the matrices elements x = np.random.randint(0,100,(5,5)) # Extract the first column x[:,0] # Extract the Second Column x[:,1] # Extract the first row x x # How to extract the 2nd and 4th row x[[2,4]] # How to extract the 1st and 4th Column y = x[:,[1,4]] ############################################################################## # 4. How to delete rows and column of a matrix. # How to delete the second row np.delete(x,,0) # How to delete the second column np.delete(x,,1) # Delete second and third row np.delete(x,[[2,3]],0) # Delete second and third column np.delete(x,[[2,3]],1)
Wiki: http://wiki.planetchili.net/index.php?title=Advanced_C%2B%2B_Programming_Tutorial_5 Patreon: https://www.patreon.com/planetchili
Views: 1841 ChiliTomatoNoodle
Check out my Blog: http://exceltraining101.blogspot.com If you've taken business class or familiar with management consulting strategies, you've probably come across this tool called a BCG Matrix. Also known as a growth-share matrix, the BCG matrix was created by Bruce Hendersen in the 70s (founder of Boston Consulting Group). It's a tool that helps you analyze companies or products based on a quadrant that shows growth rate and relative market share. You can actually create this fairly easily on Excel, so check out the video to learn how. #exceltips #exceltipsandtricks #exceltutorial #doughexcel
Views: 210173 Doug H
This video explains how to derive GLS 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: 17067 Ben Lambert
Yan Fyodorov, King's College London. Introduction not included. Lecture notes available at https://pcmi.ias.edu/sites/pcmi.ias.edu/files/Yan%20Fyodorov%20Lecture%20Notes_0.pdf How many equilibria will a large complex system, modeled by N randomly coupled autonomous nonlinear differential equations typically have? How many of those equilibria are stable, that is are local attractors of the nearby trajectories? These questions arise in many applications and can be partly answered by employing the methods of Random Matrix Theory. The lectures will outline these recent developments. Presented at the 27th Annual PCMI Summer Session, Random Matrices, held June 25 – July 15, 2017. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI). About PCMI The Institute for Advanced Study / IAS / Park City Mathematics Institute (PCMI) is designed for mathematics educators at the secondary and post-secondary level, as well as mathematics researchers and students at the post-secondary level. These groups find at PCMI an intensive mathematical experience geared to their individual needs. Moreover, the interaction among groups with different backgrounds and professional needs increases each participant’s appreciation of the mathematical community as a whole as well as the work of participants in different areas. For more information, visit https://pcmi.ias.edu
Dimitri Shlyakhtenko, University of California, Los Angeles. Lecture notes available at https://pcmi.ias.edu/sites/pcmi.ias.edu/files/Dimitri%20Shlyakhtenko%20Lecture%20Notes.pdf Voiculescu invented his free probability theory to approach problems in von Neumann algebras. A key feature of his theory is the treatment of free independence — based on the notion of free products, such as free products of groups — as a surprisingly close parallel to classical independence. Rather unexpectedly it turned out that there are deep connections between his theory and the theory of random matrices: very roughly, free probability describes certain aspects of asymptotic behavior of random matrix models. In this course, we will start with an introduction to free probability theory, discuss connections with random matrix theory, and finally describe some applications of results from random matrices in operator algebras and vice versa. Presented at the 27th Annual PCMI Summer Session, Random Matrices, held June 25 – July 15, 2017. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI). About PCMI The Institute for Advanced Study / IAS / Park City Mathematics Institute (PCMI) is designed for mathematics educators at the secondary and post-secondary level, as well as mathematics researchers and students at the post-secondary level. These groups find at PCMI an intensive mathematical experience geared to their individual needs. Moreover, the interaction among groups with different backgrounds and professional needs increases each participant’s appreciation of the mathematical community as a whole as well as the work of participants in different areas. For more information, visit https://pcmi.ias.edu