Articles containing proofs | Mathematical identities | Multilinear algebra

Lagrange's identity

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).

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Lagrange Bicentenary - Jacques Laskar's conference

Lagrange and the stability of the Solar System

From playlist Bicentenaire Joseph-Louis Lagrange

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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

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Lagrange Bicentenary - Cédric Villani's conference

From the stability of the Solar system to the stability of plasmas

From playlist Bicentenaire Joseph-Louis Lagrange

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A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

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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

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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

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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

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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

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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

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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

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Lagrange's Theorem -- Abstract Algebra 10

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From playlist Abstract Algebra

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Beltrami Identity Derivation

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

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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

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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

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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

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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

Related pages

Wedge product | Absolute value | Cauchy–Schwarz inequality | Lagrange's identity (boundary value problem) | Real coordinate space | Brahmagupta–Fibonacci identity | Dot product | Quaternion | Algebra | Dimension (vector space) | Seven-dimensional cross product | Real number | Cross product | Complex conjugate | Complex number | Q.E.D. | Binet–Cauchy identity | Jacobi identity | Commutative ring