Linear mapping
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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]
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.[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 .[5]