In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: 1. * (commutative law) 2. * (Jordan identity). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that is independent of how we parenthesize this expression. They also imply that for all positive integers m and n. Thus, we may equivalently define a Jordan algebra to be a commutative, power-associative algebra such that for any element , the operations of multiplying by powers all commute. Jordan algebras were first introduced by Pascual Jordan to formalize the notion of an algebra of observables in quantum mechanics. They were originally called "r-number systems", but were renamed "Jordan algebras" by Abraham Adrian Albert, who began the systematic study of general Jordan algebras. (Wikipedia).
A nice basis for a nilpotent operator. Jordan basis. Jordan form for an operator on a finite-dimensional complex vector space.
From playlist Linear Algebra Done Right
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
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract 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: Prove the Sherman-Morrison formula for computing a matrix inverse
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: 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
Algebra for beginners || Basics of Algebra
In this course you will learn about algebra which is ideal for absolute beginners. #Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like
From playlist Algebra
Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erzähle ich etwas über die Jordan-Zerlegung von quadratischen Matrizen bzw. die jordansche Normalform an einem Beispiel. (
From playlist Lineare Algebra
On the pioneering works of Professor I.B.S. Passi by Sugandha Maheshwari
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
Generalized Kepler Problems - Guowu Meng
Generalized Kepler Problems Guowu Meng Hong Kong University of Science & Technology; Joint Member, School of Mathematics & Natural Sciences February 4, 2011 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR For many elegant mathematical examples, one can 1) find theories behind them, 2) understand wh
From playlist Mathematics
Support Varieties for Modular Representations - Eric M. Friedlander
Members’ Seminar Topic: Support Varieties for Modular Representations Speaker: Eric M. Friedlander Affiliation: University of Southern California; Member, School of Mathematics Date: November 30, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Determinantal varieties and asymptotic expansion of Bergman kernels by Harald Upmeier
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Xavier Gómez-Mont: Grothendieck residue in the Jacobian algebra and cup product in vanishing...
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
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)
28. Similar Matrices and Jordan Form
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 28. Similar Matrices and Jordan Form License: Creative Commons BY-NC-SA More information at ht
From playlist MIT 18.06 Linear Algebra, Spring 2005
Interpreting linear graphs word problems example 2 | Algebra I | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/algebra/two-var-linear-equations-and-intro-to-functions/interpreting_linear_functions/e/interpreting-linear-graphs?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Watch the next lesson: https:
From playlist Algebra I | High School Math | Khan Academy
Pre-recorded lecture 8: Differentially non-degenerate singular points and global theorems
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)
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
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