Articles containing proofs | Functional analysis | Types of functions | Linear algebra

Sublinear function

In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional, on a vector space is a real-valued function with only some of the properties of a seminorm. Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known notion of norms, where a seminorm has all the defining properties of a norm except that it is not required to map non-zero vectors to non-zero values. In functional analysis the name Banach functional is sometimes used, reflecting that they are most commonly used when applying a general formulation of the Hahn–Banach theorem. The notion of a sublinear function was introduced by Stefan Banach when he proved his version of the Hahn-Banach theorem. There is also a different notion in computer science, described below, that also goes by the name "sublinear function." (Wikipedia).

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👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions together. To add or subtract two linear functions, w

From playlist Add and Subtract Functions

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👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions together. To add or subtract two linear functions, w

From playlist Add and Subtract Functions

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This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.

From playlist Foundational Math

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From playlist Add Subtract Multiply Divide Functions

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👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions together. To add or subtract two linear functions, w

From playlist Add Subtract Multiply Divide Functions

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From playlist PRIMA2009

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From playlist Mathematics

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From playlist Add Subtract Multiply Divide Functions

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Robustness of G-Expectation under Knightian Uncertainty - Prof. Shige Peng

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From playlist Mathematics

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Robust sublinear expanders - Matija Bucic

Short Talks by Postdoctoral Members Topic: Robust sublinear expanders Speaker: Matija Bucic Affiliation: Member, School of Mathematics Date: September 21, 2022

From playlist Mathematics

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From playlist Mathematics

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How to subtract two functions

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From playlist Add Subtract Multiply Divide Functions

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From playlist Mathematics

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Sublinear Convergence #MegaFavNumbers

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From playlist Numerical Methods

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From Robust Sublinear Expanders to Additive Number Theory via Rainbow Cycles - Matija Bucic

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From playlist Mathematics

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Definition of a Surjective Function and a Function that is NOT Surjective

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From playlist Injective, Surjective, and Bijective Functions

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Learn how to subtract two functions

👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions together. To add or subtract two linear functions, w

From playlist Add Subtract Multiply Divide Functions

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Nicolas Dirr: "Scaling Limits and Stochastic Homogenization"

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From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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From playlist Add Subtract Multiply Divide Functions

Related pages

Norm (mathematics) | Convex function | Hahn–Banach theorem | Functional analysis | Vector space | Linear algebra | Codomain | Topological vector space | Big O notation | Functional (mathematics) | Identity function | Minkowski functional | Seminorm | Stefan Banach | Concave function | Function (mathematics) | Real number | Ordered vector space | Balanced set | Subadditivity | Complex number | Q.E.D. | Triangle inequality