Functions and mappings | Functional analysis

Discontinuous linear map

In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation). If the spaces involved are also topological spaces (that is, topological vector spaces), then it makes sense to ask whether all linear maps are continuous. It turns out that for maps defined on infinite-dimensional topological vector spaces (e.g., infinite-dimensional normed spaces), the answer is generally no: there exist discontinuous linear maps. If the domain of definition is complete, it is trickier; such maps can be proven to exist, but the proof relies on the axiom of choice and does not provide an explicit example. (Wikipedia).

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Ch7 Pr2: Linear Maps

A map T between vector spaces which satisfies: * the addition condition T(x+y) = T(x) + T(y) and * the scalar multiplication condition T(lambda x) = lambda T(x) is called a "linear map". In the first part of this video we see how to show a map is linear; in the second part we see how t

From playlist Mathematics 1B (Algebra)

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What is a linear equation

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

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What is the slope of a linear equation

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

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Linear Maps | Linear Algebra

In this lecture, we discuss the definition of a linear map, relating it to the definition of a vector space. We also give an elementary example, illustrating how to verify that a map is linear or not linear. Video Notes: https://theorembmath.files.wordpress.com/2020/02/linear-maps-definit

From playlist Linear Algebra

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Identifying Linear Functions

Define linear functions. Use function notation to evaluate linear functions. Learn to identify linear function from data, graphs, and equations.

From playlist Algebra 1

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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

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Dynamics and Bifurcations of Piecewise - Smooth ODEs (Lecture 4) by David simpson

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From playlist Dynamics of Complex systems 2018

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👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

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Examples of Linear Maps

Linear Algebra: Here are a few problems on linear maps. Part 1: Are the following maps L:R^3 to R^3 linear? (a) L(x, y, z) = (x+1, x-y-2, y-z), (b) L(x, y, z) = (x + 2y, x-y-2z, 0). Part 2: Suppose L:R^3 to R^2 is linear and defined on the standard basis by L(e1) = (1, 2), L(e2) =

From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics

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DDPS | Model reduction of partial differential equations via optimization-based feature tracking

In this DDPS talk from June 24, 2021, University of Notre Dame assistant professor Matthew Zahr introduces an optimization-based model reduction framework to solve conservation laws with parametrized, discontinuous solution features such as shock waves. The proposed reduction framework s

From playlist Data-driven Physical Simulations (DDPS) Seminar Series

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Stability of the set of quantum states - S. Weis - Workshop 2 - CEB T3 2017

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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

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From playlist Surface group representations and Projective Structures (2018)

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Flows on surfaces are one of the fundamental examples of dynamical systems, studied since Poincaré; area preserving flows arise from many physical and mathematical examples, such as the Novikov model of electrons in a metal, unfolding of billiards in polygons, pseudo-periodic topology. In

From playlist Corinna Ulcigrai - Chaotic Properties of Area Preserving Flows

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On the (in)stability of the identity map in optimal transportation - Yash Jhaveri

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From playlist Mathematics

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COLLOQUIUM DEEP LEARNING AND COMPUTATIONS OF PDES SPEAKER: Siddhartha Mishra (Professor of Applied Mathematics, ETH ZĂĽrich, Switzerland) DATE & TIME: Mon, 27 June 2022, 15:30 to 17:00 VENUE: Online Colloquium ABSTRACT Partial Differential Equations (PDEs) are ubiquitous in the scien

From playlist ICTS Colloquia

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Planar N = 4 at High Loops and Large Multiplicity by Andrew McLeod

PROGRAM RECENT DEVELOPMENTS IN S-MATRIX THEORY (ONLINE) ORGANIZERS: Alok Laddha, Song He and Yu-tin Huang DATE: 20 July 2020 to 31 July 2020 VENUE:Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through online

From playlist Recent Developments in S-matrix Theory (Online)

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Proper Actions and Representation Theory Part 1

Professor Toshiyuki Kobayashi, University of Tokyo, Japan

From playlist Distinguished Visitors Lecture Series

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What is everything you need to know to graph an equation in slope intercept form

👉 Learn about graphing linear equations. A linear equation is an equation whose highest exponent on its variable(s) is 1. i.e. linear equations has no exponents on their variables. The graph of a linear equation is a straight line. To graph a linear equation, we identify two values (x-valu

From playlist ⚡️Graph Linear Equations | Learn About

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