= Homogeneous function
{title2=$f(\lambda x)=\lambda^k f(x)$}
{wiki}
A <function> is homogeneous of degree $k$ when rescaling its arguments by a common <scalar> $\lambda$ rescales its value by $\lambda^k$, whenever the arguments and that power are defined. For integer $k$ over a <vector space>, one can require every nonzero scalar; a <homogeneous polynomial> gives an example. On a domain stable under positive real rescaling, the positive-scaling version allows real $k$. Degree-one <positive homogeneity> is the convention used for <norms> and many <convex functions>. The <Euler theorem for homogeneous functions> turns this scaling law into a differential identity for a <differentiable function>.
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