[[Mathematics MOC]]
# Homogenous function
A function is said to be **homogenous of degree $n$** iff ==multiplying its arguments by a scalar $s$ is equivalent to multiplying the result by a given power of the scalar $s^n$==, #m/def/general 
i.e.
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$$
\begin{align*}
f(s \vab v) = s^n f(\vab v)
\end{align*}
$$
for any scalar $s$.
A [[Linear map|linear map]] is by definition homogenous of degree 1.

The properties of homogenous functions allow for the solution of a special class of differential equation.
See [[Homogenous first-order differential equation]].

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