Functional analysis | Linear algebra | Norms (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the , or , which may also be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "" in the homogeneity axiom.It can also refer to a norm that can take infinite values, or to certain functions parametrised by a directed set. (Wikipedia).
From playlist Linear Algebra Ch 6
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
13C Norm and Distance in Euclidean n Space
Norm and distance in Euclidean n-Space.
From playlist Linear Algebra
Matrix Norms : Data Science Basics
What does it mean to take the norm of a matrix? Vector Norms Video: https://www.youtube.com/watch?v=5fN2J8wYnfw Eigenvalues and Eigenvectors Video: https://www.youtube.com/watch?v=glaiP222JWA
From playlist Data Science Basics
From playlist Linear Algebra Ch 6
Euclidean n Space. Norm and distance in n space.
From playlist Linear Algebra
Understanding Vector Norms in Machine Learning (L1 and L2 norms, unit balls, and NumPy)
This video explains the concept of norm for vectors from the machine learning perspective. Norm is a function that maps a vector to a positive value and a special case is the L-p norm, where p is greater than or equal to 1. Examples include the popular L1 and L2 norms in machine learning a
From playlist Mathematics for Machine Learning - Dr. Data Science Series
Lecture with Ole Christensen. Kapitler: 00:00 - Introduction; 06:45 - Vector Spaces; 07:15 - Example 1; 12:00 - Mathematical Tool - Fourier Transform; 17:00 - Example 2; 20:00 - Example 3; 23:00 - New Concept - Norm; 27:45 - Lemma 2.1.2 - The Opposite Triangle Inequality; 35:15 - Convergen
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Metric dimension reduction: A snapshot of the Ribe program – Assaf Naor – ICM2018
Plenary Lecture 16 Metric dimension reduction: A snapshot of the Ribe program Assaf Naor Abstract: The purpose of this article is to survey some of the context, achievements, challenges and mysteries of the field of ‘metric dimension reduction’, including new perspectives on major older
From playlist Plenary Lectures
Lecture with Ole Christensen. Kapitler: 00:00 - Boundedness/Supremum; 05:00 - Example; 08:00 - Maximum Value; 09:00 - Example: Sup Vs. Max; 12:45 - Theorem: Maximum Is Attained On Closed And Bounded Intervals; 15:30 - Vectorspace Of Continuous Functions; 22:00 - Norm On C[A,B]; 36:45 - Exa
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Lecture with Ole Christensen. Kapitler: 00:00 - Banach Spaces; 06:30 - Cauchy Sequences; 12:00 - Def: Banach Space; 15:45 - Examples; 17:15 - C[A,B] Is Banach With Proof; 36:30 - Ex: Sequence Space L^1(N); 46:45 - Sequence Space L^p(N);
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Orthonormal Bases Vs Fourier Series Part 2
Lecture with Ole Christensen. Kapitler: 00:00 - Proof Of Thrm 4.7.2 Continued; 11:00 - Connection To Fourier Series; 11:15 - L2(-Pi,Pi); 16:00 - Complex Fourier Series; 17:45 - Convergence?; 35:45 - Parseval Identity;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Lecture with Ole Christensen. Kapitler: 00:00 - Def: Hilbert Space; 05:00 - New Example Of A Hilbert Space; 15:15 - Operators On Hilbert Spaces; 20:00 - Example 1; 24:00 - Example 2; 38:30 - Riesz Representation Theorem; 43:00 - Concerning Physics;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Lp Spaces On The Real Line part 2
Lecture with Ole Christensen. Kapitler: 00:00 - Remarks On Banach Spaces; 08:00 - Proof That Cc Is Not A Banach Space; 31:00 - Applications; 38:30 - Integral Operators;
From playlist DTU: Mathematics 4 Real Analysis | CosmoLearning.org Math
Metric Spaces - Lectures 3 & 4: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 2nd of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Two decentralised learning problems: Sketching and policy evaluation - Justin Romberg, Georgia Tech
This workshop - organised under the auspices of the Isaac Newton Institute on “Approximation, sampling and compression in data science” — brings together leading researchers in the general fields of mathematics, statistics, computer science and engineering. About the event The workshop ai
From playlist Mathematics of data: Structured representations for sensing, approximation and learning
Metric Spaces - Lectures 1 & 2: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 1st of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 9 - VMLS norm
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares