In mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation where is the transpose of . Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(n,R).) The simple Lie groups were classified by Wilhelm Killing and Élie Cartan in the 1880s and 1890s. At that time, no special use was made of the fact that the group structure can be defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin. In the 1950s, Armand Borel constructed much of the theory of algebraic groups as it exists today. One of the first uses for the theory was to define the Chevalley groups. (Wikipedia).
The Special Linear Group is a Subgroup of the General Linear Group Proof
The Special Linear Group is a Subgroup of the General Linear Group Proof
From playlist Abstract Algebra
Michael Wibmer: Etale difference algebraic groups
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 Algebraic and Complex Geometry
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. Topic covered: Vectors: Basic vectors notation, adding, scaling (0:0
From playlist Linear Algebra
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The General Linear Group, The Special Linear Group, The Group C^n with Componentwise Multiplication
From playlist Abstract Algebra
Linear Algebra for Beginners | Linear algebra for machine learning
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. In this course you will learn most of the basics of linear algebra wh
From playlist Linear Algebra
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation
Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be view
From playlist Linear Algebra
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
A Non-flag Arithmetic Regularity Lemma and Counting Lemma - Daniel Altman
Special Year Informal Seminar Topic: A Non-flag Arithmetic Regularity Lemma and Counting Lemma Speaker: Daniel Altman Affiliation: University of Oxford Date: March 10, 2023 We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the gener
From playlist Mathematics
Is the variety of singular tuples of matrices a null cone? - Viswambhara Makam
Computer Science/Discrete Mathematics Seminar II Topic: Is the variety of singular tuples of matrices a null cone? - Speaker: Viswambhara Makam Affiliation: Member, School of Mathematics Date: February 25, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Calista Bernard - Applications of twisted homology operations for E_n-algebras
An E_n-algebra is a space equipped with a multiplication that is commutative up to homotopy. Such spaces arise naturally in geometric topology, number theory, and mathematical physics; some examples include classifying spaces of braid groups, spaces of long knots, and classifying spaces of
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Pablo Linares & Markus Tempelmayr - A tree-free construction of the structure group
We present a new approach to regularity structures, and in particular to the construction of the structure group, which replaces the tree-based framework of Hairer by a more Lie-geometric setting. We consider the space of pairs (a,p), where a is a placeholder for the nonlinearity and p is
From playlist Research Spotlight
Matthias Seiß, Universität Kassel
April 16, Matthias Seiß, Universität Kassel Differential Invariants and the Classical Groups
From playlist Spring 2021 Online Kolchin Seminar in Differential Algebra
Chelsea Walton, "An Invitation to Noncommutative Algebra," the 2021 NAM Claytor-Woodard Lecture
Chelsea Walton, Rice University, gives the NAM Claytor-Woodard Lecture on "An invitation to Noncommutative Algebra," on January 9, 2021 at the Joint Mathematics Meetings
From playlist Useful math
Why was Connes' embedding conjecture refuted and there are still no known... -Michael Chapman
Stability and Testability Topic: Why was Connes' embedding conjecture refuted and there are still no known non-hyperlinear groups? Speaker: Michael Chapman Affiliation: Hebrew University Date: March 24, 2021 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q)
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q) In this lecture we back up and deploy the basis elements we eliminated in the su(2) and so(3) algebras when we enforced the determinants to be equal to 1. This expands the algebras to u(2) and o(3) and generates the groups U(2) a
From playlist Lie Groups and Lie Algebras