In numerical linear algebra, a Jacobi rotation is a rotation, Qkℓ, of a 2-dimensional linear subspace of an n-dimensional inner product space, chosen to zero a symmetric pair of off-diagonal entries of an n×n real symmetric matrix, A, when applied as a similarity transformation: It is the core operation in the Jacobi eigenvalue algorithm, which is numerically stable and well-suited to implementation on parallel processors. Only rows k and ℓ and columns k and ℓ of A will be affected, and that A′ will remain symmetric. Also, an explicit matrix for Qkℓ is rarely computed; instead, auxiliary values are computed and A is updated in an efficient and numerically stable way. However, for reference, we may write the matrix as That is, Qkℓ is an identity matrix except for four entries, two on the diagonal (qkk and qℓℓ, both equal to c) and two symmetrically placed off the diagonal (qkℓ and qℓk, equal to s and −s, respectively). Here c = cos θ and s = sin θ for some angle θ; but to apply the rotation, the angle itself is not required. Using Kronecker delta notation, the matrix entries can be written Suppose h is an index other than k or ℓ (which must themselves be distinct). Then the similarity update produces, algebraically, (Wikipedia).
What is the difference between rotating clockwise and counter clockwise
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations
Determining clockwise vs counter clockwise rotations
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations
Why is the Rotation Matrix Orthogonal? | Classical Mechanics
For any rotation matrix R, we usually know that it's transpose is equal to it's inverse, so that R^T R is equal to the identity matrix. This is due to the fact that we take the rotation matrix to be orthogonal. But why do we assume that rotation matrices are orthogonal? In this video, we w
From playlist Classical Mechanics
This is the other case. The first one was rotation about yb and xa, or if you like x into a and y into b, this one is rotation about xb and ya or x into b and y into a. Now I have a strange feeling that there are again an inifinite number of mixed cases, but I will not think about that now
From playlist Fractal
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta
Theory of numbers: Jacobi symbol
This lecture is part of an online undergraduate course on the theory of numbers. We define the Jacobi symbol as an extension of the Legendre symbol, and show how to use it to calculate the Legendre symbol fast. We also briefly mention the Kronecker symbol. For the other lectures in t
From playlist Theory of numbers
some julia dynamics combined with a rotation in the direction of mandelbrot.
From playlist Fractal
Martin Gander: On the invention of iterative methods for linear systems
HYBRID EVENT Recorded during the meeting "1Numerical Methods and Scientific Computing" the November 9, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on
From playlist Numerical Analysis and Scientific Computing
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
William Minicozzi: Singularities and diffeomorphisms – Rigidity Lecture Two
Speaker info: William P. Minicozzi II is the Singer Professor of Mathematics at MIT. Throughout an enduring collaboration with Tobias H. Colding, he has resolved a number of major open problems in several areas of geometric analysis. Colding and Minicozzi received jointly the AMS Oswald Ve
From playlist MATRIX-SMRI Symposium: Singularities in Geometric Flows
Parallel session 8 by Dave Constantine
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
60 Sritharan - Stochastic Navier-Stokes equations - solvability & control
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have
From playlist Winter School on Stochastic Analysis and Control of Fluid Flow
Nov. 17, Chapter 18 (Semi-direct products)
From playlist Fall 2020 Course
Some remarks on symplectic forms (in physics and mathematics) - Leon A. Takhtajan [2018]
Name: Leon A. Takhtajan Event: Program: Poisson geometry of moduli spaces, associators and quantum field theory Event URL: view webpage Title: Some remarks on symplectic forms (in physics and mathematics) Date: 2018-05-02 @2:00 PM Location: 102 http://scgp.stonybrook.edu/video_portal/vide
From playlist Mathematics
Universality aspects in numerical computation - Percy Deift
Percy Deift Columbia Univeristy November 7, 2013 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Hamiltonian Structure of 2D Fluid Dynamics with Broken Parity by Sriram Ganeshan
DISCUSSION MEETING : HYDRODYNAMICS AND FLUCTUATIONS - MICROSCOPIC APPROACHES IN CONDENSED MATTER SYSTEMS (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, India), Keiji Saito (Keio University, Japan) and Tomohiro Sasamoto (Tokyo Institute of Technology, Japan) DATE : 06 September 2021 to
From playlist Hydrodynamics and fluctuations - microscopic approaches in condensed matter systems (ONLINE) 2021
Sinh-Gordon equation and application to the geometry of CMC surfaces - Laurent Hauswirth
Workshop on Mean Curvature and Regularity Topic: Sinh-Gordon equation and application to the geometry of CMC surfaces. Speaker: Laurent Hauswirth Affiliation: Université de Marne-la-Vallée Date: November 7, 2018 For more video please visit http://video.ias.edu
From playlist Workshop on Mean Curvature and Regularity
Rotations in degrees for counter and clockwise directions
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations