ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D1587
Euclidean real function slope

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) $$X \neq \emptyset$$ (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 $$\forall \, x \in \mathbb{R}^N : \mathcal{L}(x) = L x$$