In mathematics, and more specifically in linear algebra, a linear map is a mapping V\to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism.

What is linear transformation with example?

Therefore T is a linear transformation. Two important examples of linear transformations are the zero transformation and identity transformation. The zero transformation defined by T(→x)=→(0) for all →x is an example of a linear transformation. Similarly the identity transformation defined by T(→x)=→(x) is also linear.

What is meant by a linear transformation?

A linear transformation is a function from one vector space to another that respects the underlying (linear) structure of each vector space. A linear transformation is also known as a linear operator or map. ... The two vector spaces must have the same underlying field.