Normed Linear Spaces | Introduction, L1 and L2 Norms
In this video, we introduce norms and normed linear spaces (normed vector spaces). These feature heavily in data science and machine learning applications and so we use an example from the data science to highlight the application of normed linear spaces. Chapters 0:00 - Introduction 0:35
From playlist Approximation Theory
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
The formal definition of a vector space.
From playlist Linear Algebra Done Right
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
From playlist Unlisted LA Videos
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
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Complete metric space: example & proof
This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.
From playlist Mathematical analysis and applications
DeepMind x UCL RL Lecture Series - Deep Reinforcement Learning #2 [13/13]
Research Engineer Matteo Hessel covers general value functions, GVFs as auxiliary tasks, and explains how to deal with scaling issues in algorithms. Slides: https://dpmd.ai/deeprl2 Full video lecture series: https://dpmd.ai/DeepMindxUCL21
From playlist Learning resources
Damaris Schindler: Interactions of analytic number theory and geometry - lecture 1
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction. Recording during the meeting "Geometric and Analytic Methods for Rational Points" the April 17, 2019 at the Centre In
From playlist Algebraic and Complex Geometry
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Stochastic Homogenization (Lecture 2) by Andrey Piatnitski
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Roger Heath-Brown: The Determinant Method, Lecture II
Lecture 1 will set the background for the course, describing the problem of counting rational points on algebraic varieties, the phenomena that can arise, and some of the results which have been proved. Lecture 2 will prove the basic theorem of the p-adic Determinant Method. Lecture 3 will
From playlist Harmonic Analysis and Analytic Number Theory
Peter Lax: Abstract Phragmen-Lindelöf theorem & Saint Venant’s principle
Programme for the Abel Lectures 2005: 1. "Abstract Phragmen-Lindelöf theorem & Saint Venant’s principle" by Abel Laureate 2005 Peter D. Lax, New York University 2. "Systems of conservation laws" by Professor Sebastian Noelle, CMA Oslo/ RWTH Aachen 3. "Hyperbolic equations and spectral geom
From playlist Abel Lectures
Can Mathematically Darkened Colors look Good? Least Squares method #SoME1
Imagine that you are a designer. You got tasked with designing a new web application. You create a palette of colors, and you want to iterate on that palette fast. But once the primary colors are changed, a lot of auxiliary colors need to be recreated. Turns out there’s no automatic
From playlist Summer of Math Exposition Youtube Videos
Xiaoying Dai - Convergent orthogonality preserving appoximations of the Kohn-Sham orbitals
Recorded 05 May 2022. Xiaoying Dai of the Chinese Academy of Sciences presents "Convergent orthogonality preserving appoximations of the Kohn-Sham orbitals" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: To obtain convergent numerical approximati
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Maryna Viazovska - 1/6 Automorphic Forms and Optimization in Euclidean Space
Hadamard Lectures 2019 The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and I
From playlist Hadamard Lectures 2019 - Maryna Viazovska - Automorphic Forms and Optimization in Euclidean Space
Giuseppe Buttazzo : Dirichlet-Neumann shape optimization problems
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 Control Theory and Optimization
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4