Let $\mathbb{R}^N$ and $\mathbb{R}^M$ each be a D1512: Standard euclidean real norm-topological vector space such that

(i)	$X \subseteq \mathbb{R}^N$ is a D5612: Euclidean real set
(ii)	\begin{equation} X \neq \emptyset \end{equation}
(iii)	$x_0 \in X$ is a D92: Limit point of $X$ in $\mathbb{R}^N$
(iv)	$f : X \to \mathbb{R}^M$ is a D1416: Differentiable euclidean real function at $x_0$
(v)	$\mathcal{L} : \mathbb{R}^N \to \mathbb{R}^M$ is a D111: Euclidean real function derivative for $f$ at $x_0$

A D4571: Real matrix $L \in \mathbb{R}^{M \times N}$ is a slope matrix for $f$ at $x_0$ if and only if \begin{equation} \forall \, x \in \mathbb{R}^N : \mathcal{L}(x) = L x \end{equation}