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 …

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 …

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

Linear maps are the most important concept in linear algebra. This video breaks down a proof in linear algebra to help you understand how to define a linear map completely.

For finite-dimensional vector spaces, it seems that a mapping A:Fn → Fm is linear if and only if A is defined as the entries of u being the coefficients of a linear combination of n vectors in Fm

What is a Linear Map? A linear map, also known as a linear transformation, is a mathematical function that maps vectors from one vector space to another while preserving the operations of …

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 …

Thus, a linear map is said to be operation preserving. In other words, it does not matter whether the linear map is applied before (the right hand sides of the above examples) or after (the left …

In order to be able to compare vector spaces, we use mappings between vector spaces that respect the vector space structure, the so-called linear maps. We begin with the definition of a …

Linear maps can often be represented as matrices, and simple examples include rotation and reflection linear transformations. In the language of category theory, linear maps are the …