In mathematics, and more specifically in linear algebra, a linear map (or linear mapping) is a particular kind of function between vector spaces, which respects the basic operations of …

Definition of linear map, with several explanations, examples and solved exercises.

This page titled 6: Linear Maps is shared under a not declared license and was authored, remixed, and/or curated by Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling.

Dec 26, 2022 · Functions with this property, which we’re going to define shortly, are called linear maps. They allow us to do something similar to the finite set example above: for example, if …

Jul 23, 2025 · Linear mapping is a mathematical operation that transforms a set of input values into a set of output values using a linear function. It is often used as a preprocessing step to …

The following theorem says that the matrix representation map relative to any given bases has another important property: that it relates composition of linear maps with multiplication of their …

In algebraic terms, a linear map is said to be a homomorphism of vector spaces. An invertible homomorphism where the inverse is also a homomorphism is called an isomorphism.

The result above shows that a matrix can be seen as a (linear) map from the “input” space to the “output” space . Both points of view (matrices as simple collections of vectors, or as linear …

Aug 25, 2025 · Linear maps are special maps between vector spaces that are compatible with the vector space structure. They are one of the most important concepts of linear algebra and …

In Linear Algebra we focus on a special class of maps, namely linear maps – the ones which respect our fundamental operations, addition of vectors and multiplication by scalars.