In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute. In particular there is natural definition of the determinant for them and most linear algebra theorems like Cramer's rule, Cayley–Hamilton theorem, etc. hold true for them. Any matrix with commuting elements is a Manin matrix. These matrices have applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems. Manin matrices are particular examples of Manin's general construction of "non-commutative symmetries" which can be applied to any algebra.From this point of view they are "non-commutative endomorphisms" of polynomial algebra C[x1, ...xn].Taking (q)-(super)-commuting variables one will get (q)-(super)-analogs of Manin matrices, which are closely related to quantum groups. Manin works were influenced by the quantum group theory.He discovered that quantized algebra of functions Funq(GL) can be defined by the requirement that T and Tt are simultaneously q-Manin matrices.In that sense it should be stressed that (q)-Manin matrices are defined only by half of the relations of related quantum group Funq(GL), and these relations are enough for many linear algebra theorems. (Wikipedia).
Vectors, Linear Transformations, and Vector Fields | Mastering Manim Chapter 6
In this video, we learn how to utilize the Linear Algebra features of Manim including graphing vectors and their coordinates, Linear Transformations, and Vector fields. TIMESTAMPS: 0:00 - What is Linear Algebra 0:11 - Linear Plane as a VectorScene 1:45 - Graphing Vectors and labeling thei
From playlist Getting Started with Manim Cairo
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Factorial Sums #wordlesswednesday (visual proof)
This is a short, animated visual proof demonstrating a finite sum involving products of factorials. #mathshorts #mathvideo #math #numbertheory #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #factorial #squares #factoradic #discretemath
From playlist Finite Sums
Sieve Of Eratosthenes (visualized)
This is a visualization of the Sieve of Eratosthenes used to find the primes up to 900. We only need to check for divisibility by primes up to 30, which is the square root of 900 so we find these primes relatively quickly. #manim #sieve #eratosthenes #visualmath #math #mtbos #primes #numbe
From playlist Number Theory
Matrix Groups (Abstract Algebra)
Matrices are a great example of infinite, nonabelian groups. Here we introduce matrix groups with an emphasis on the general linear group and special linear group. The general linear group is written as GLn(F), where F is the field used for the matrix elements. The most common examples
From playlist Abstract Algebra
The Manim Cast #2 - The Overall Structure of Manim and your first Basic Animations [feat. @vcubingx]
Support the channel by signing up on Brilliant for FREE using the link https://brilliant.org/FlammableMaths ! =D Subscribe to @vcubingx! https://www.youtube.com/channel/UCv0nF8zWevEsSVcmz6mlw6A Manim Cast Playlist: https://www.youtube.com/watch?v=Jfgtl-AW5Oc&list=PLN2B6ZNu6xmeRb0GPGW7dN05u
From playlist The Manim Cast
Andrew Sutherland, Arithmetic L-functions and their Sato-Tate distributions
VaNTAGe seminar on April 28, 2020. License: CC-BY-NC-SA Closed captions provided by Jun Bo Lau.
From playlist The Sato-Tate conjecture for abelian varieties
Francesca Balestrieri, The arithmetic of zero-cycles on products of K3 surfaces and Kummer varieties
VaNTAGe seminar, March 9, 2021
From playlist Arithmetic of K3 Surfaces
Complex Matrices ( An intuitive visualization )
Complex Matrices are not given enough credit for what they do and even when they are used its often introduced as an foreign entity. This video was made to shed light on such a misinterpreted topic. Timestamps 00:00 - Introduction 00:11 - Matrix 00:45 - Complex Number 02:50 - Complex Ma
From playlist Summer of Math Exposition Youtube Videos
Marta Pieropan, The split torsor method for Manin’s conjecture
See https://tinyurl.com/y98dn349 for an updated version of the slides with minor corrections. VaNTAGe seminar 20 April 2021
From playlist Manin conjectures and rational points
Holly Krieger, Equidistribution and unlikely intersections in arithmetic dynamics
VaNTAGe seminar on May 26, 2020. License: CC-BY-NC-SA. Closed captions provided by Marley Young.
From playlist Arithmetic dynamics
On Sharifi’s Conjectures and Generalizations by Emmanuel Lecouturier
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)
Will Sawin, The freeness alternative to thin sets in Manin's conjecture
VaNTAGe seminar, May 4, 2021 License: CC-BY-NC-SA
From playlist Manin conjectures and rational points
Definition of a matrix | Lecture 1 | Matrix Algebra for Engineers
What is a matrix? Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers
CDH methods in K-theory and Hochschild homology - Charles Weibel
Charles Weibel Rutgers University; Member, School of Mathematics November 11, 2013 This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assumi
From playlist Mathematics
Bjorn Poonen, Heuristics for the arithmetic of elliptic curves
VaNTAGe seminar on Sep 1, 2020. License: CC-BY-NC-SA. Closed captions provided by Brian Reinhart.
From playlist Rational points on elliptic curves
2 Construction of a Matrix-YouTube sharing.mov
This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.
From playlist Linear Algebra
Bianca Viray, The Brauer group and the Brauer-Manin obstruction on K3 surfaces
VaNTAGe seminar, February 23, 2021
From playlist Arithmetic of K3 Surfaces
The Manim Cast #4 - (3D) Graphing, Camera, Parametric Functions/Surfaces [feat. @vcubingx ]
SUbscribe to @vcubingx ! https://www.youtube.com/watch?v=g_5P9AW_seg Manim Cast Playlist: https://www.youtube.com/watch?v=Jfgtl-AW5Oc&list=PLN2B6ZNu6xmeRb0GPGW7dN05u2OXD_6h6 Engineering Clock! :D https://teespring.com/flammable-math-clock Viveks Used Code: https://gist.github.com/vivek314
From playlist The Manim Cast
Yuri Tschinkel, Height zeta functions
VaNTAGe seminar May 11, 2021 License: CC-BY-NC-SA
From playlist Manin conjectures and rational points