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homogeneous function
Definition 1.
Suppose $V,\,W$ are a vector spaces over $\mathbbmss{R}$, and $f\colon V\to W$ is a mapping.

If there exists an $r\in\mathbbmss{R}$, such that
$f(\lambda v)=\lambda^{r}f(v)$ for all $\lambda\in\mathbbmss{R}$ and $v\in V$, then $f$ is a homogeneous function of degree $r$.

If there exists an $r\in\mathbbmss{R}$, such that
$f(\lambda v)=\lambda^{r}f(v)$ for all $\lambda\in\mathbbmss{R}$ and $v\in V$, then $f$ is absolutely homogeneous function of degree $r$.

If there exists an $r\in\mathbbmss{R}$, such that
$f(\lambda v)=\lambda^{r}f(v)$ for all $\lambda\geq 0$ and $v\in V$, then $f$ is a positively homogeneous function of degree $r$.
Notes
For any homogeneous function as above, $f(0)=0$.
Related:
HomogeneousPolynomial, SubLinear
Synonym:
positively homogeneous function of degree, homogeneous function of degree,positively homogeneous function
Type of Math Object:
Definition
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