Ring theory | Quadratic forms | Clifford algebras
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations. Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing. They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (pseudo-)Riemannian Clifford algebras, as distinct from symplectic Clifford algebras. (Wikipedia).
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
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
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist 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 2e: Confirming All the 'Tivities
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
Linear Algebra Full Course for Beginners to Experts
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 may be basically viewed as the application of l
From playlist Linear Algebra
Linear Algebra 11p: Some Matrices Are Not Invertible - I.e. They Don't Have an Inverse
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
LC001.03 - Clifford algebras and matrix factorisations
A brief introduction to Clifford algebras, their universal property, how to construct a Clifford algebra from the Hessian of a quadratic form, and how modules over that Clifford algebra determine matrix factorisations. This video is a recording made in a virtual world (https://www.roblox.
From playlist Metauni
Taylor Dupuy | Spheres Packings in Hyperbolic Space
African Mathematics Seminar | 2 September 2020 Virtually hosted by the University of Nairobi Visit our webpage: https://sites.google.com/view/africa-math-seminar Sponsor: International Science Programme
From playlist Seminar Talks
Linear Algebra 1.3 Matrices and Matrix Operations
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
Matrix factorisations and quantum error correcting codes
In this talk Daniel Murfet gives a brief introduction to matrix factorisations, the bicategory of Landau-Ginzburg models, composition in this bicategory, the Clifford thickening of a supercategory and the cut operation, before coming to a simple example which shows the relationship between
From playlist Metauni
Christian Voigt: Clifford algebras, Fermions and categorification
Given the fundamental role of Dirac operators in K-homology and K-theory, it can be argued that "categorified Dirac operators" should be crucial for the understanding of elliptic cohomology. However, the actual construction of such operators seems a challenging open problem. In this talk
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)
We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersecti
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Landau-Ginzburg - Seminar 5 - From quadratic forms to bicategories
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Dan Murfet starts with quadratic forms and introduces Clifford algebras, their modules and bimodules and explains how these fit into a bicategory
From playlist Metauni
Daniel Murfet - The third dawn of reason
This informal talk outlines an argument that our time will become one of the most important in the history of logic, because of the growing importance of geometric algebra in deep learning (essentially realising the vision of Boole in 1854). This talk was part of the first Festival of Mat
From playlist Metauni
Jeongwan Haah - Nontrivial Clifford QCAs - IPAM at UCLA
Recorded 01 September 2021. Jeongwan Haah of Microsoft Research presents "Nontrivial Clifford QCAs" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: An interesting role of QCA is that it can disentangle a Hamiltonian while quantum circuits cannot. We
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Linear Algebra 6i: Linear Dependence Example 5 - Vectors in ℝⁿ
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