Linear mapping

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 (number) 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 formula_1.