# What is a linear transformation definition?

**What is a linear transformation definition?**In

**byebyebimari**

Introduction to **linear transformations**. In **linear** algebra, a **transformation** between two vector spaces is a rule that assigns a vector in one space to a vector in the other space. **Linear transformations** are **transformations** that satisfy a particular property around addition and scalar multiplication.

.

Regarding this, what is the meaning of 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.

Likewise, what is linear transformation with example? Also, a **linear transformation** always maps lines to lines (or to zero). The main **example** of a **linear transformation** is given by matrix multiplication. Given an matrix , define , where is written as a column vector (with coordinates).

Subsequently, question is, what makes something a linear transformation?

In mathematics, a **linear** map (also called a **linear mapping**, **linear transformation** or, in some contexts, **linear** function) is a **mapping** V → W between two modules (for example, two vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

How do you know if a transformation is linear?

It is simple enough to identify **whether** or not a given function f(x) is a **linear transformation**. Just look at each term of each component of f(x). **If** each of these terms is a number times one of the components of x, then f is a **linear transformation**. are **linear transformations**.

**Trending Answer**

**ByeByeBimari**

**ByeByeBimari**

**ByeByeBimari**