Articles containing proofs | Mathematical identities | Multilinear algebra
In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: which applies to any two sets {a1, a2, ..., an} and {b1, b2, ..., bn} of real or complex numbers (or more generally, elements of a commutative ring). This identity is a generalisation of the Brahmagupta–Fibonacci identity and a special form of the Binet–Cauchy identity. In a more compact vector notation, Lagrange's identity is expressed as: where a and b are n-dimensional vectors with components that are real numbers. The extension to complex numbers requires the interpretation of the dot product as an inner product or Hermitian dot product. Explicitly, for complex numbers, Lagrange's identity can be written in the form:involving the absolute value. Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate space Rn and its complex counterpart Cn. Geometrically, the identity asserts that the square of the volume of the parallelepiped spanned by a set of vectors is the Gram determinant of the vectors. (Wikipedia).
Lagrange Bicentenary - Alain Albouy's conference
Lagrange and the N body Problem
From playlist Bicentenaire Joseph-Louis Lagrange
Lagrange Bicentenary - Jacques Laskar's conference
Lagrange and the stability of the Solar System
From playlist Bicentenaire Joseph-Louis Lagrange
Lagrange Bicentenary - Luigi Pepe's conference
Scientific biography of Joseph Louis Lagrange Part one, Lagrange in Turin : calculus of variation and vibrating sring Part two, Lagrange in Paris : didactical works and Dean for Scientific activities at the National Institute
From playlist Bicentenaire Joseph-Louis Lagrange
Lagrange Bicentenary - Cédric Villani's conference
From the stability of the Solar system to the stability of plasmas
From playlist Bicentenaire Joseph-Louis Lagrange
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
From playlist Physics ONE
Interview d'Aline BONAMI au CIRM
Aline BONAMI, interviewée lors d'un passage à Marseille, au CIRM, parle de son parcours, de ses activités, de la place des femmes dans la recherche en mathématiques, etc. Interview/Réalisation : Stéphanie Vareilles (CIRM) Tournage : bibliothèque du CIRM Décembre 2013 - Marseille - Luminy
From playlist Lagrange Days at CIRM
Norbert Verdier : When He was one hundred Years old!
In this Talks we will don’t speak about Joseph-Louis Lagrange (1736-1813) but about Lagrange’s reception at the nineteenth Century. “Who read Lagrange at this Times?”, “Why and How?”, “What does it mean being a mathematician or doing mathematics at this Century” are some of the questions o
From playlist Lagrange Days at CIRM
Lagrange's Theorem and Index of Subgroups | Abstract Algebra
We introduce Lagrange's theorem, showing why it is true and follows from previously proven results about cosets. We also investigate groups of prime order, seeing how Lagrange's theorem informs us about every group of prime order - in particular it tells us that any group of prime order p
From playlist Abstract Algebra
Abstract Algebra - 7.2 LaGrange’s Theorem and Consequences
In this video we explore Lagrange's Theorem, which tells us some important information about both the order of a subgroup of a group, as well as the number of distinct cosets we can expect given a certain subgroup H. Video Chapters: Intro 0:00 LaGrange's' Theorem 0:07 Consequences of LaGr
From playlist Abstract Algebra - Entire Course
Subderivatives and Lagrange's Approach to Taylor Expansions | Algebraic Calculus Two | Wild Egg
The great Italian /French mathematician J. L. Lagrange had a vision of analysis following on from the algebraic approach of Euler (and even of Newton before them both). However Lagrange's insights have unfortunately been largely lost in the modern treatment of the subject. It is time to re
From playlist Algebraic Calculus Two
Cosets and Lagrange’s Theorem - The Size of Subgroups (Abstract Algebra)
Lagrange’s Theorem places a strong restriction on the size of subgroups. By using a device called “cosets,” we will prove Lagrange’s Theorem and give some examples of its power. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We re
From playlist Abstract Algebra
Lagrange's Theorem -- Abstract Algebra 10
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From playlist Abstract Algebra
The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).
From playlist Physics
Lec 16 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
Lecture 16: Elastic Constitutive Relations in U. L. Formulation Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Nonlinear Finite Element Analysis
Summary: an example covering ALL group theory concepts!! | Essence of Group Theory
The summary of the entire video series! After a quick recap on all the important concepts covered in the series, we see a very interesting, yet a bit involved example to see how these concepts can be applied to prove an interesting result. The concepts that we used are: (1) The correspond
From playlist Essence of Group Theory
Untold connection: Lagrange and ancient Chinese problem
Lagrange interpolating polynomial and an ancient Chinese problem is actually connected! It is a surprising connection, and a very inspiring one at the same time. It tells us that Mathematics has much more to discover! Lagrange interpolating polynomial is normally see as a statistical meth
From playlist Modular arithmetic
GT3. Cosets and Lagrange's Theorem
Abstract Algebra: Let G be a group with subgroup H. We define an equivalence relation on G that partitions G into left cosets. We use this partition to prove Lagrange's Theorem and its corollary. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theor
From playlist Abstract Algebra