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Linear mapping facts for kids

Kids Encyclopedia Facts

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: VW 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:

f(\mathbf{x}+\mathbf{y}) = f(\mathbf{x})+f(\mathbf{y}) \!
f(\alpha \mathbf{x}) = \alpha f(\mathbf{x}) \!

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 L(V, W).

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