Matrices

Birkhoff factorization

In mathematics, Birkhoff factorization or Birkhoff decomposition, introduced by George David Birkhoff, is the factorization of an invertible matrix M with coefficients that are Laurent polynomials in z into a product M = M+M0M−, where M+ has entries that are polynomials in z, M0 is diagonal, and M− has entries that are polynomials in z−1. There are several variations where the general linear group is replaced by some other reductive algebraic group, due to Alexander Grothendieck. Birkhoff factorization implies the Birkhoff–Grothendieck theorem of that vector bundles over the projective line are sums of line bundles. Birkhoff factorization follows from the Bruhat decomposition for affine Kac–Moody groups (or loop groups), and conversely the Bruhat decomposition for the affine general linear group follows from Birkhoff factorization together with the Bruhat decomposition for the ordinary general linear group. (Wikipedia).

Video thumbnail

Factoring trinomials #2 difference of two squares

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Factoring a binomial using the difference of two squares

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Factoring a binomial using distributive property

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Factoring Binomials | Step by Step | Part 2

👉 In this video I will show you how to factor a binomial by working through four different examples. The first two examples we practice factoring out the GCF, and then move to factoring using a difference of two squares and last but not least factoring using a difference of two cubes. 👏SU

From playlist Understand Factoring - Step by Step

Video thumbnail

Factoring Trinomials | Step by Step | Part 3

👉In this video you will learn how to factor a trinomial into a product of two binomials. We will investigate factoring out the GCF, factoring with a is not one and factoring trinomials to a higher power. 👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclogan?sub_conf

From playlist Understand Factoring - Step by Step

Video thumbnail

Ergodicity of the Weil-Petersson geodesic flow (Lecture - 1) Keith Burns

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

Video thumbnail

Ellipses of small eccentricity are determined by their Dirichlet... - Steven Morris Zelditch

Analysis Seminar Topic: Ellipses of small eccentricity are determined by their Dirichlet (or, Neumann) spectra Speaker: Steven Morris Zelditch Affiliation: Northwestern University Date: April 28, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Factoring a quadratic by diamond method

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Lecture 5 | Topics in String Theory

(February 7, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses again on black holes and how light behaves around a black hole. He uses his own theories to mathematically explain the behavior of a black hole and the area around it. In the last of cou

From playlist Lecture Collection | Topics in String Theory (Winter 2011)

Video thumbnail

Learning how to factor a binomial using the difference of two squares

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Factoring using the difference of two squares with multiple terms, 64m^2 - 9y^2

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Dynamics in Dimension 3: Geometry of Birkhoff Sections

Etienne Ghys l'École Normale Supérieure de Lyon October 30, 2013 Birkhoff sections have been invented... by Poincaré in his work on celestial mechanics. Birkhoff made an extensive use of this concept in dynamical systems. Sometimes, one can find surfaces transverse to the trajectories of a

From playlist Mathematics

Video thumbnail

[BOURBAKI 2019] Infinité d’hypersurfaces minimales en basses dimensions - Rivière - 15/06/19

Tristan RIVIÈRE Infinité d’hypersurfaces minimales en basses dimensions, d’après Fernando Codá Marques, André Neves et Antoine Song Une conjecture de Shing Tung Yau du début des années 80 pose le problème de l’existence d’une infinité de surfaces minimales (points critiques de la foncti

From playlist BOURBAKI - 2019

Video thumbnail

Lecture 4 | Topics in String Theory

(January 31, 2011) Leonard Susskind gives a lecture on string theory and particle physics that focuses on the geometry of a black hole near the horizon. He describes how standard concepts from quantum physics can explain the physics that occur at this point. In the last of course of this

From playlist Lecture Collection | Topics in String Theory (Winter 2011)

Video thumbnail

Factoring using difference of two squares

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Joel Hass - Lecture 4 - Algorithms and complexity in the theory of knots and manifolds - 21/06/18

School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro

From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

Video thumbnail

Jean-Pierre Ramis - The Mano Decompositions...

The Mano Decompositions and the Space of Monodromy Data of the q-Painlevé V I Equation The talk is based upon a joint work with Y. OHYAMA and J. SAULOY. Classically the space of Monodromy data (or character variety) of PV I (the sixth Painlevé differential equation) is the space of linear

From playlist Resurgence in Mathematics and Physics

Video thumbnail

How to factor using the area of a rectangle with difference of two squares

👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe

From playlist Factor Quadratic Expressions | Difference of Two Squares

Video thumbnail

Pierre Dehornoy: Wich geodesic flows are left-handed?

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Dynamical Systems and Ordinary Differential Equations

Related pages

Bruhat decomposition | Riemann–Hilbert problem | Line bundle | Birkhoff–Grothendieck theorem | Loop group | Invertible matrix | Linear group | Vector bundle