Mathematical proofs | Category theory | Homological algebra | Mathematical terminology
In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the same result. It is said that commutative diagrams play the role in category theory that equations play in algebra. (Wikipedia).
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
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 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 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
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
Commutative algebra 61: Examples of regular local rings
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 some examples of regular local rings. We first give an example of a regular local ring that is not geometrically regul
From playlist Commutative algebra
This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle. http://mathispower4u.yolasite.com/
From playlist Vectors
In this video, we prove certain formal properties of THH, for example that it has a universal property in the setting of commutative rings. We also show base-change properties and use these to compute THH of perfect rings. Feel free to post comments and questions at our public forum at h
From playlist Topological Cyclic Homology
Lecture 6: HKR and the cotangent complex
In this video, we discuss the cotangent complex and give a proof of the HKR theorem (in its affine version) Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-m
From playlist Topological Cyclic Homology
Category Theory 1.6 : Natural Transformations
In this video, I will introduce natural transformations between (covariant) functors, and the category of functors. Translate This Video : http://www.youtube.com/timedtext_video?v=YIAaZxGOyl0&ref=share Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://
From playlist Category Theory
Landau-Ginzburg - Seminar 3 - Introduction to Bicategories
This seminar series is about the bicategory of Landau-Ginzburg models LG, hypersurface singularities and matrix factorisations. In this seminar Rohan Hitchcock introduces bicategories and gives the example of rings, bimodules and bimodule maps. The webpage for this seminar is https://meta
From playlist Metauni
ITHT: Part 9- The Homotopy Category
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheHomotopyCategory Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtube Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Nam
From playlist Introduction to Homotopy Theory
Commutative algebra 9 (Euclidean domains)
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 describe one method of visualizing rings by drawing pictures of their points, and use this to show that the ring of Gaussia
From playlist Commutative algebra
Higher Algebra 5: Slices and filtered colimits
In this video, we provide further properties of the derived category of an abelian category. Along the way we discuss slice categories and filtered colimits. This is the fifth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our pub
From playlist Higher Algebra
Category Theory 2.1 : Comma and Slice Categories
In this video, I will introduce the comma category created by two functors, and also the slice and co-slice categories C/a and a/C. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fematikaq
From playlist Category Theory
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
Category Theory 2.1.1 : Universality of the Comma Category
In this video, I prove a universal property relating to the comma category between two functors. This was filmed a while ago. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika Email : fematikaqna@gma
From playlist Category Theory
Lec 5 - Phys 237: Gravitational Waves with Kip Thorne
Watch the rest of the lectures on http://www.cosmolearning.com/courses/overview-of-gravitational-wave-science-400/ Redistributed with permission. This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and
From playlist Caltech: Gravitational Waves with Kip Thorne - CosmoLearning.com Physics
Teun van Nuland: Cyclic cocycles and one-loop corrections of the spectral action
Talk by Teun van Nuland in the Global Noncommutative Geometry Seminar (Americas) on October 28, 2022. https://globalncgseminar.org/talks/tba-37/
From playlist Global Noncommutative Geometry Seminar (Americas)
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