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.^[1][2][3]

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 (number) α in K, the following two conditions are satisfied:

Sometimes, a linear mapping is called a linear function.^[4] 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 👁 {\displaystyle L(V,W)}
.^[5]

• Homomorphism
• Transformation