Ring theory | Multilinear algebra | Polynomials | Algebras
In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is a commutative algebra over K that contains V, and is, in some sense, minimal for this property. Here, "minimal" means that S(V) satisfies the following universal property: for every linear map f from V to a commutative algebra A, there is a unique algebra homomorphism g : S(V) → A such that f = g ∘ i, where i is the inclusion map of V in S(V). If B is a basis of V, the symmetric algebra S(V) can be identified, through a canonical isomorphism, to the polynomial ring K[B], where the elements of B are considered as indeterminates. Therefore, the symmetric algebra over V can be viewed as a "coordinate free" polynomial ring over V. The symmetric algebra S(V) can be built as the quotient of the tensor algebra T(V) by the two-sided ideal generated by the elements of the form x ⊗ y − y ⊗ x. All these definitions and properties extend naturally to the case where V is a module (not necessarily a free one) over a commutative ring. (Wikipedia).
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Symmetric matrices - eigenvalues & eigenvectors
Free ebook http://tinyurl.com/EngMathYT A basic introduction to symmetric matrices and their properties, including eigenvalues and eigenvectors. Several examples are presented to illustrate the ideas. Symmetric matrices enjoy interesting applications to quadratic forms.
From playlist Engineering Mathematics
In this video we construct a symmetric group from the set that contains the six permutations of a 3 element group under composition of mappings as our binary operation. The specifics topics in this video include: permutations, sets, groups, injective, surjective, bijective mappings, onto
From playlist Abstract algebra
Definition of the Symmetric Group
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of the Symmetric Group
From playlist Abstract Algebra
Linear Algebra 11z: Introduction to Symmetric Matrices
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
The Symmetric Difference is Associative Proof Video
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Symmetric Difference is Associative Proof Video. This is video 3 on Binary Operations.
From playlist Abstract Algebra
Linear Algebra - Lecture 41 - Diagonalization of Symmetric Matrices
In this lecture, we investigate the diagonalization of symmetric matrices.
From playlist Linear Algebra Lectures
Eigenvectors of Symmetric Matrices Are Orthogonal
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Higher Algebra 10: E_n-Algebras
In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin
From playlist Higher Algebra
QED Prerequisites Geometric Algebra 3: The symmetric part
In this lesson we begin unpealing the spacetime product of two 4-vectors. The spacetime product can be split into a symmetric and anti-symmetric part and it is critical to understand what each of these two parts represents. We begin with the symmetric part. lease consider supporting thi
From playlist QED- Prerequisite Topics
Matt Hogancamp: Soergel bimodules and the Carlsson-Mellit algebra
The dg cocenter of the category of Soergel bimodules in type A, morally speaking, can be thought of as a categorical analogue of the ring of symmetric functions, as in joint work of myself, Eugene Gorsky, and Paul Wedrich. Meanwhile, the ring of symmetric functions is the recipient of acti
From playlist Workshop: Monoidal and 2-categories in representation theory and categorification
Pre-recorded lecture 9: Homogeneous linear Nijenhuis operators and left-symmetric algebras
MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)
Nijenhuis Geometry Chair's Talk 2 (Alexey Bolsinov)
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Chair's Talk 2 (Alexey Bolsinov) 8 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 February 2022 Week
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
In this video, we prove certain formal properties of THH, for example that it has a universal property in the setting of commutative rings. We also show base-change properties and use these to compute THH of perfect rings. Feel free to post comments and questions at our public forum at h
From playlist Topological Cyclic Homology
Omar León Sánchez, University of Manchester
December 17, Omar León Sánchez, University of Manchester A Poisson basis theorem for symmetric algebras
From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 5
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 4/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Diagonalizing a symmetric matrix. Orthogonal diagonalization. Finding D and P such that A = PDPT. Finding the spectral decomposition of a matrix. Featuring the Spectral Theorem Check out my Symmetric Matrices playlist: https://www.youtube.com/watch?v=MyziVYheXf8&list=PLJb1qAQIrmmD8boOz9a8
From playlist Symmetric Matrices
Seminar on Applied Geometry and Algebra (SIAM SAGA): Bernd Sturmfels
Date: Tuesday, February 9 at 11:00am EST (5:00pm CET) Speaker: Bernd Sturmfels, MPI MiS Leipzig / UC Berkeley Title: Linear Spaces of Symmetric Matrices. Abstract: Real symmetric matrices appear ubiquitously across the mathematical sciences, and so do linear spaces of such matrices. We
From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)