# Linear mapping facts for kids

In mathematics (particularly in linear algebra), a **linear mapping** (or linear transformation) is a mapping *f* between vector spaces that preserves addition and scalar multiplication.

## Definition

Let *V* and *W* be vector spaces over the same field *K*. A function *f*: *V* → *W* is said to be a *linear mapping* if for any two vectors **x** and **y** in *V* and any scalar α in *K*, the following two conditions are satisfied:

Sometimes, a linear mapping is called a linear function. However, in basic mathematics, a linear function means a function whose graph is a line. The set of all linear mappings from the vector space *V* to vector space *W* can be written as .

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Linear mapping Facts for Kids. *Kiddle Encyclopedia.*