Morphisms | Additive functions | Ring theory

Additive map

In algebra, an additive map, -linear map or additive function is a function that preserves the addition operation: for every pair of elements and in the domain of For example, any linear map is additive. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial. More formally, an additive map is a -module homomorphism. Since an abelian group is a -module, it may be defined as a group homomorphism between abelian groups. A map that is additive in each of two arguments separately is called a bi-additive map or a -bilinear map. (Wikipedia).

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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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From playlist Determining Inverse Functions

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This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Determining Inverse Functions

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This video explains how to determine the additive inverse of a given integers. http://mathispower4u.com

From playlist Sets of Numbers/Properties of Real Numbers

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From playlist Number Theory

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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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From playlist Geometry

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Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.

From playlist Learning medical statistics with python and Jupyter notebooks

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From playlist New perspectives on K- and L-theory

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From playlist What is a Tensor?

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From playlist QED- Prerequisite Topics

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From playlist Topology

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Linear Algebra - Part 18 - Linear Maps (Definition)

Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.

From playlist Linear Algebra

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From playlist Linear Algebra Done Right

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From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

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From playlist Oxford Linear Algebra

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Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Additive Group of Integers Modulo n

From playlist Abstract Algebra

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Linear Algebra - Part 18 - Linear Maps (Definition) [dark version]

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From playlist Linear Algebra [dark version]

Related pages

Pointwise | Linear map | Additive group | Domain of a function | Abstract algebra | Group homomorphism | Vector space | Function (mathematics) | Cauchy's functional equation | Real number | Ring (mathematics) | Abelian group | Module homomorphism | Module (mathematics) | Additive polynomial | Homogeneous function