linear map

Mapping that preserves the operations of addition and scalar multiplication

EntityQ207643

Also known as linear mapping · linear transformation · linear function · linear homomorphism · linear mapped

Subclass of: function
, additive map
, homogeneous function

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of function between vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example of a linear map is an matrix, which takes vectors in -dimensions into vectors in -dimensions in a way that is compatible with addition of vectors, and multiplication of vectors by scalars. When the two vector spaces are the same, a linear map is also called a linear transformation or linear endomorphism.

Overview

All data

37 statements · 16% with external sources · numbers in brackets are citations

Said to be the same as: linear operator
matrix
Different from: linear function
Studied by: linear algebra
Manifestation of: proportionality
Defining formula: T(\alpha \mathbf{x} + \beta \mathbf{y}) = \alpha T(\mathbf{x}) + \beta T(\mathbf{y}), \quad \forall \alpha, \beta \in \mathbb{R}, \forall \mathbf{x}, \mathbf{y} \in \operatorname{dom}(T)
In defining formula: T symbol represents: linear map
Has characteristic: proportionality

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Source last edited October 2, 2026. AIDB refreshes this page daily.

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AIDB. (2026). linear map (Q207643). Retrieved from https://aidb.si/e/linear-map-Q207643