Lie algebras | Representation theory | Matrices

Cartan matrix

In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices in the context of Lie algebras were first investigated by Wilhelm Killing, whereas the Killing form is due to Cartan. (Wikipedia).

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Column space of a matrix

We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the

From playlist Introducing linear algebra

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What is a Matrix?

What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

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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

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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

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Linear Algebra for Computer Scientists. 12. Introducing the Matrix

This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order

From playlist Linear Algebra for Computer Scientists

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Understanding Matrices and Matrix Notation

In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start

From playlist Mathematics (All Of It)

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Cartesian coordinates | Lecture 2 | Vector Calculus for Engineers

Defines Cartesian coordinates, unit vectors, the position vector and the displacement vector. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my channel: http://

From playlist Vector Calculus for Engineers

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Quivers for symmetrizable Cartan matrices and algebraic Lie theory – C. Geiß – ICM2018

Lie Theory and Generalizations | Algebra Invited Lecture 7.11 | 2.6 Quivers with relations for symmetrizable Cartan matrices and algebraic Lie theory Christof Geiß Abstract: We give an overview of our effort to introduce (dual) semicanonical bases in the setting of symmetrizable Cartan m

From playlist Lie Theory and Generalizations

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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

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Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions

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 Analysis and its Applications

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Vector spaces | Lecture 16 | Matrix Algebra for Engineers

Definition of a vector space. 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

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Xin Li: Cartan subalgebras in C*-algebras

This talk is about the notion of Cartan subalgebras introduced by Renault, based on work of Kumjian. We explain how Cartan algebras build a bridge between dynamical systems and operator algebras, and why this notion might be interesting for the structure theory of C*-algebras as well. The

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

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Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan #shorts

Elementary Theory of Analytic Functions of One or Several Complex Variables by Henri Cartan #shorts Full Review: https://youtu.be/5JJzHUKyxrE This is the book on amazon:https://amzn.to/380wqF7 (note this is my affiliate link) Book Review #shorts: https://www.youtube.com/playlist?list=PL

From playlist Book Reviews #shorts

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Oldschool Complex Analysis Book

Oldschool Complex Analysis Book This is the book on amazon: https://amzn.to/2pTP39K (note this is my affiliate link, I earn a small percentage from qualifying purchases) This is an absolute classic. The author of this book was a founding member of the Bourbaki Group and lived to be 104 y

From playlist Cool Math Stuff

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Kevin Buzzard (lecture 18/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

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On the crossroads of enumerative geometry and representation theory – Andrei Okounkov – ICM2018

Plenary Lecture 4 On the crossroads of enumerative geometry and geometric representation theory Andrei Okounkov Abstract: The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts that reflect a certain range of developmen

From playlist Plenary Lectures

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Holomorphic Cartan geometries on simply connected manifolds by Sorin Dumitrescu

Discussion Meeting Complex Algebraic Geometry ORGANIZERS: Indranil Biswas, Mahan Mj and A. J. Parameswaran DATE:01 October 2018 to 06 October 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore The discussion meeting on Complex Algebraic Geometry will be centered around the "Infosys-ICT

From playlist Complex Algebraic Geometry 2018

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Matrix addition

How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y

From playlist Introducing linear algebra

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Math Book Power Tower

Let's look at some math books:) I tried to pick books which are good and/or famous to some extent. All of these books are pretty good. Some are good for beginners and some are definitely not good for beginners. These are the books on amazon. Linear algebra by Strang https://amzn.to/3tAy

From playlist Book Reviews

Related pages

Commutator | G2 (mathematics) | Dynkin diagram | Modular representation theory | Semisimple algebra | Simple Lie algebra | Associative algebra | String theory | Degrees of freedom (physics and chemistry) | Affine Lie algebra | Élie Cartan | Simple Lie group | Diagonal matrix | Root system | Soliton | Determinant | Composition series | Kac–Moody algebra | Principal indecomposable module | Cycle graph | Mathematics | Integer | Square matrix | Intersection number | Cartan subalgebra | Euclidean space | Lie algebra | Symmetric matrix | Linear combination | Dimensional reduction | Fundamental representation | Killing form