Let \(\mathbb{K}\) be \(\mathbb{R}\) or \(\mathbb{C}\). We call a function \(f\colon \mathbb{R}^d\to \mathbb{K}\) homogeneous of degree \(k\in \mathbb{N}\) if for every \(t\in \mathbb{R}\) and \(x\in \mathbb{R}^d\)
\[ f(tx)=t^k f(x). \]Let \(\mathbb{K}\) be \(\mathbb{R}\) or \(\mathbb{C}\). We call a function \(f\colon \mathbb{R}^d\to \mathbb{K}\) homogeneous of degree \(k\in \mathbb{N}\) if for every \(t\in \mathbb{R}\) and \(x\in \mathbb{R}^d\)
\[ f(tx)=t^k f(x). \]