Matrix Theory: Let A be an nxn matrix with complex entries. We show that the commutant of A has dimension greater than or equal to n. The key step is to show the result for the Jordan canonical form of A.
From playlist Matrix Theory
Commutative algebra 1 (Introduction)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the
From playlist Commutative algebra
Commutative algebra 2 (Rings, ideals, modules)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. This lecture is a review of rings, ideals, and modules, where we give a few examples of non-commutative rings and rings without
From playlist Commutative algebra
You might find that for certain groups, the commutative property hold. In this video we will assume the existence of such a group and prove a few properties that it may have, by way of some example problems.
From playlist Abstract algebra
Commutative algebra 27 (Associated primes)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We show that every finitely generated module M over a Noetherian ring R can broken up into modules of the form R/p for p prime
From playlist Commutative algebra
EDIT: At 11:50, r^2(l-k) should be r^2l. At 14:05, index for top one should be n-2, not 2n-2. Abstract Algebra: We define the commutator subgroup for a group G and the corresponding quotient group, the abelianization of G. The main example is the dihedral group, which splits into tw
From playlist Abstract Algebra
Semigroups and Abelian Algebraic Structures
Thesis: https://www.researchgate.net/publication/328163392_The_Cayley_type_theorem_for_semigroups Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Paper's Playlist: https://www.youtube.com/watch?v=nvYqkhZFzyY&lis
From playlist Bachelor's Paper
From Magmas to Fields: a trippy excursion through algebra - SoME2 3b1b
A gentle introduction to the most basic definitions in Algebra (and how to make them stick forever). If you always struggled to remember what a field is this video is for you. You will learn about: 0:00 This videos aim 1:20 Sets 1:52 Magmas 3:15 Semigroups 4:39 Monoids 5:22 Groups 6:04 Co
From playlist Summer of Math Exposition 2 videos
What is a group? -- Abstract Linear Algebra 3
⭐Highly Suggested Linear Algebra books⭐ Linear Algebra, an introduction to abstract mathematics: https://amzn.to/3rkp4Wc Linear Algebra Done Right: https://amzn.to/3rkp4Wc The Manga Guide to Linear Algebra: https://amzn.to/3HnS59o A First Course in Linear Algebra: http://linear.ups.edu/ Li
From playlist Abstract Linear Algebra
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
CTNT 2020 - A virtual tour of Magma
This video is part of a series of videos on "Computations in Number Theory Research" that are offered as a mini-course during CTNT 2020. In this video, we take a virtual tour of Magma, the computational algebra system, paying special attention to its number theory capabilities. Please clic
From playlist CTNT 2020 - Computations in Number Theory Research
Kiran S. Kedlaya: Frobenius structures on hypergeometric equations: computational methods
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: Current implementations of the computation of L-functions associated to hypergeometric motives in Magma and Sage rely on a p-adic trace formula
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"
Mathieu ANEL - Toposes are commutative rings
Abstract: In this talk, we shall develop the point of view comparing (higher) toposes to commutative rings. We shall then see how the corresponding integral and differential calculus are related respectively to Verdier duality and Goodwillie calculus of functors.
From playlist Topos à l'IHES
https://www.math.ias.edu/files/media/agenda.pdf More videos on http://video.ias.edu
From playlist Mathematics
Yang Shi: Normalizer theory of Coxeter groups and discrete integrable systems
Abstract: Formulation of the Painleve equations and their generalisations as birational representations of affine Weyl groups provides us with an elegant and efficient way to study these highly transcendental, nonlinear equations. In particular, it is well-known that discrete evolutions of
From playlist Integrable Systems 9th Workshop
Commutative algebra 53: Dimension Introductory survey
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We give an introductory survey of many different ways of defining dimension. Reading: Section Exercises:
From playlist Commutative algebra
Donald Cartwright : Construction of lattices defining fake projective planes - lecture 2
Recording during the meeting "Ball Quotient Surfaces and Lattices " the February 25, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Ma
From playlist Algebraic and Complex Geometry
When Does Exponentiation Commute? (Part 1)
In this video, I'll show how one can find pairs of numbers that can be commuted under exponentiation. That is, we can find pairs of numbers such that x^y = y^x. We will take this equation, x^y = y^x and parametrize it to find these (x,y) pairs. It turns out that there are infinitely many n
From playlist Math
Introducing Algebraic Structures: Magmas and Groupoids [ N is closed under + ]
Thesis: https://www.researchgate.net/publication/328163392_The_Cayley_type_theorem_for_semigroups Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Paper's Playlist: https://www.youtube.com/watch?v=nvYqkhZFzyY&lis
From playlist Bachelor's Paper
5B Commutative Law of Matrix Multiplication-YouTube sharing.mov
A closer look at three examples of the Commutative Law of Matrix Multiplication.
From playlist Linear Algebra