In mathematics, the rank of a differentiable map between differentiable manifolds at a point is the rank of the derivative of at . Recall that the derivative of at is a linear map from the tangent space at p to the tangent space at f(p). As a linear map between vector spaces it has a well-defined rank, which is just the dimension of the image in Tf(p)N: (Wikipedia).
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
Definition of Rank and showing Rank(A) = Dim Col(A) In this video, I define the notion of rank of a matrix and I show that it is the same as the dimension of the column space of that matrix. This is another illustration of the beautiful interplay between linear transformations and matrice
From playlist Linear Equations
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
(0.3.101) Exercise 0.3.101: Classifying Differential Equations
This video explains how to classify differential equations based upon their properties https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Ex 1: Determine Higher Order Derivatives
This video provides an example of how to determine the first, second, third, and fourth derivative of a function. Complete Video List at http://www.mathispower4u.com
From playlist Higher Order Differentiation
Steven Bradlow - Exotic components of surface group representation varieties
Steven Bradlow Exotic components of surface group representation varieties, and their Higgs bundle avatars Moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. For representations into complex semisimple Lie groups,
From playlist Maryland Analysis and Geometry Atelier
Differential Equatons: Find the Order and Classify as Linear or Nonlinear
This video explains how to determine the order of a differential equation and how to determine if it is linear or nonlinear. http://mathispower4u.com
From playlist Introduction to Differential Equations
Yanli Song: Higher index theorem for proper actions of Lie groups
Talk by Yanli Song in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on May 6, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Ana Romero: Effective computation of spectral systems and relation with multi-parameter persistence
Title: Effective computation of spectral systems and their relation with multi-parameter persistence Abstract: Spectral systems are a useful tool in Computational Algebraic Topology that provide topological information on spaces with generalized filtrations over a poset and generalize the
From playlist AATRN 2022
Thomas KRAJEWSKI - Connes-Kreimer Hopf Algebras...
Connes-Kreimer Hopf Algebras : from Renormalisation to Tensor Models and Topological Recursion At the turn of the millenium, Connes and Kreimer introduced Hopf algebras of trees and graphs in the context of renormalisation. We will show how the latter can be used to formulate the analogu
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
F. Boarotto - Normal forms around regular abnormal curves in rank-two distributions (Part 2)
Let (M, ∆) be a rank-two sub-Riemannian structure on a smooth manifold M, and let x, y be any two points on M. In this talk I will present some recent results concerning the description of the set Ω(y), of all the horizontal curves joining x and y, in the vicinity of a rank-two-nice singul
From playlist Journées Sous-Riemanniennes 2018
Title: Differential Fields—A Model Theorist's View May 2016 Kolchin Seminar Workshop
From playlist May 2016 Kolchin Seminar Workshop
Anthony Nouy: Adaptive low-rank approximations for stochastic and parametric equations [...]
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 Numerical Analysis and Scientific Computing
Higgs Bundles and Higher Teichmüller Spaces - Brian Collier
Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: Higgs Bundles and Higher Teichmüller spaces Speaker: Brian Collier Affiliation: University of California, Riverside Date: September 17, 2022 The Teichm\"uller space of a compact surface S is re
From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday
Title: Density of Rational Points on Transcendental Varieties
From playlist Differential Algebra and Related Topics VII (2016)