Linear mapping
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In mathematics, 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 α in K, the following two conditions are satisfied:
| [math]\displaystyle{ f(\mathbf{x}+\mathbf{y}) = f(\mathbf{x})+f(\mathbf{y}) \! }[/math] |
| [math]\displaystyle{ f(\alpha \mathbf{x}) = \alpha f(\mathbf{x}) \! }[/math] |
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.