In mathematics, a linear map or linear function f(x) is a function that satisfies the two properties:[1]

- Additivity [Additivity]: f(x + y) = f(x) + f(y).
- Homogeneity [Homogeneity] of degree 1: f(αx) = α f(x) for all α.
These properties are known as the superposition principle. In this definition, x is not necessarily a real number, but can in general be an element of any vector space.

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## References

“Linearity.” 2022.

*Wikipedia*, December. https://en.wikipedia.org/w/index.php?title=Linearity&oldid=1128635807.