This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
From playlist Contributed talks One World Symposium 2020
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
The formal definition of a vector space.
From playlist Linear Algebra Done Right
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
Foundations of QM: Introduction Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussing the material on the forums: https://www.patreon.com/XYLYXYLYX
From playlist Mathematical Foundations of Quantum Mechanics
Index Theory, survey - Stephan Stolz [2018]
TaG survey series These are short series of lectures focusing on a topic in geometry and topology. May_8_2018 Stephan Stolz - Index Theory https://www3.nd.edu/~math/rtg/tag.html (audio fixed)
From playlist Mathematics
Konrad Polthier (7/27/22): Boundary-sensitive Hodge decompositions
Abstract: We provide a theoretical framework for discrete Hodge-type decomposition theorems of piecewise constant vector fields on simplicial surfaces with boundary that is structurally consistent with decomposition results for differential forms on smooth manifolds with boundary. In parti
From playlist Applied Geometry for Data Sciences 2022
MAST30026 Lecture 19: Duality and Hilbert space
I began by proving the universal property of the completion of a normed space. I then discussed characterisations of finite-dimensionality for vector spaces, introduced the continuous linear dual for normed spaces and the operator norm, and stated the duality theorem or L^p spaces which sa
From playlist MAST30026 Metric and Hilbert spaces
Alexei Davydov: Condensation of anyons in topological states of matter & structure theory
Condensation of anyons in topological states of matter and structure theory of E_2-algebras Abstract: The talk will be on the algebraic structure present in both parts of the title. This algebraic story is most pronounced for E2-algebras in the category of 2-vector spaces (also known as b
From playlist SMRI Seminars
Michał Lipiński 7/20/20: Conley-Morse-Forman theory for generalized combinatorial multivector fields
Title: Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces Abstract: The combinatorial approach to dynamics has its origins in the Forman's (1998) concept of a combinatorial vector field. The original motivation of Forman was the presen
From playlist ATMCS/AATRN 2020
Ezra Miller (12/4/2018): Real multiparameter persistent homology
Persistent homology with multiple continuous parameters presents fundamental challenges different from those arising with one real or multiple discrete parameters. Existing algebraic theories apply either for discrete parameters or for one continuous parameter. In part, the difficulty ar
From playlist AATRN 2018
Luis Scoccola (5/3/21): Approximate and discrete vector bundles
Synchronization problems, such as the problem of reconstructing a 3D shape from a set of 2D projections, can often be modeled by principal bundles. Similarly, the application of local PCA to a point cloud concentrated around a manifold approximates the tangent bundle of the manifold. In th
From playlist TDA: Tutte Institute & Western University - 2021
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
Benson Farb, Part 1: Permutations and polynomiality in algebra and topology
29th Workshop in Geometric Topology, Oregon State University, June 28, 2012
From playlist Benson Farb: 29th Workshop in Geometric Topology