Orthogonal polynomials | Articles containing proofs
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special cases. The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes. They appear in a wide variety of fields: numerical analysis (quadrature rules), probability theory, representation theory (of Lie groups, quantum groups, and related objects), enumerative combinatorics, algebraic combinatorics, mathematical physics (the theory of random matrices, integrable systems, etc.), and number theory. Some of the mathematicians who have worked on orthogonal polynomials include Gábor Szegő, Sergei Bernstein, Naum Akhiezer, Arthur Erdélyi, Yakov Geronimus, Wolfgang Hahn, Theodore Seio Chihara, Mourad Ismail, Waleed Al-Salam, Richard Askey, and Rehuel Lobatto. (Wikipedia).
Linear Algebra 7.1 Orthogonal Matrices
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Determine if the Vectors are Orthogonal
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determine if the Vectors are Orthogonal
From playlist Calculus
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
In this last part of the orthogonality extravaganza, I show how to use our orthogonality-formula to find the full Fourier series of a function. I also show to what function the Fourier series converges too. In a future video, I'll show you how to find the Fourier sine/cosine series of a fu
From playlist Orthogonality
Find an Orthogonal Projection of a Vector Onto a Line Given an Orthogonal Basis (R2)
This video explains how t use the orthogonal projection formula given subset with an orthogonal basis. The distance from the vector to the line is also found.
From playlist Orthogonal and Orthonormal Sets of Vectors
Proof: Orthogonal Matrices Satisfy A^TA=I
One way to characterize orthogonal matrices is to say that a matrix orthogonal if and only if A transpose times A is the identity matrix. In this video, we prove this result using basic matrix calculations and the definition of orthonormal vectors. Learning Linear Algebra playlist: https:
From playlist Learning Linear Algebra
Orthogonal Matrix Example (Ch5 Pr28)
We look at a rotation matrix as an example of a orthogonal matrix. This is Chapter 5 Problem 28 from the MATH1141/MATH1131 Algebra notes. Presented by Daniel Mansfield from the School of Mathematics and Statistics at UNSW.
From playlist Mathematics 1A (Algebra)
11I Orthogonal Projection of a Vector
The Orthogonal Projection of one vector along another.
From playlist Linear Algebra
Francesco Mezzadri: Moments of Random Matrices and Hypergeometric Orthogonal Polynomials
We establish a new connection between moments of n×n random matrices $X_{n}$ and hypergeometric orthogonal polynomials. Specifically, we consider moments $\mathbb{E}\mathrm{Tr} X_n^{-s}$ as a function of the complex variable $s\in\mathbb{C}$, whose analytic structure we describe completely
From playlist Jean-Morlet Chair - Grava/Bufetov
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite ...
Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (17.02.2017) In t
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Gaussian Quadrature 1: Summary of Legendre Polynomials
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Polynomial Regression Models (Part A)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
Maurice Duits (KTH) -- Part 2: Multiple orthogonal polynomial ensembles
The Strong Szegö Limit Theorem for Toeplitz determinants implies a CLT for linear statistics for eigenvalues of a CUE matrix. The first part of the talk will be an overview of results on various extensions of the Strong Szegö Limit theorem to determinants of truncated exponentials of ban
From playlist Integrable Probability Working Group
From playlist Contributed talks One World Symposium 2020
Mod-01 Lec-21 Projection Theorem in a Hilbert Spaces (Contd.) and Approximation
Advanced Numerical Analysis by Prof. Sachin C. Patwardhan,Department of Chemical Engineering,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Advanced Numerical Analysis | CosmoLearning.org
Sarah Post: Rational extensions of superintegrable systems, exceptional polynomials & Painleve eq.s
Abstract: In this talk, I will discuss recent work with Ian Marquette and Lisa Ritter on superintegable extensions of a Smorodinsky Winternitz potential associated with exception orthogonal polynomials (EOPs). EOPs are families of orthogonal polynomials that generalize the classical ones b
From playlist Integrable Systems 9th Workshop
Diane Holcomb: Random Orthogonal Polynomials: From matrices to point processes
For the commonly studied Hermitian random matrix models there exist tridiagonal matrix models with the same eigenvalue distribution and the same spectral measure $v_{n}$ at the vector $e_{1}$. These tridiagonal matrices give recurrence coefficients that can be used to build the family of r
From playlist Probability and Statistics
Principal axes theorem + orthogonal matrices
Free ebook http://tinyurl.com/EngMathYT A basic introduction to orthogonal matrices and the principal axes theorem. Several examples are presented involving a simplification of quadratic (quadric) forms. A proof is also given.
From playlist Engineering Mathematics
Sabine Jansen - Duality, intertwining and orthogonal polynomials for continuum...
Sabine Jansen (LMU Munich) Duality, intertwining and orthogonal polynomials for continuum interacting particle systems. Duality is a powerful tool for studying interacting particle systems, i.e., continuous-time Markov processes describing many particles say on the lattice Zd. In recent
From playlist Large-scale limits of interacting particle systems