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Let $k\in\mathbb N$, $H_i$ be a (finite-dimensional, if necessary) $\mathbb R$-Hilbert space for $i\in I:=\{1,\ldots,k\}$, $H:=\bigotimes_{i\in I}H_i$ denote the tensor product$^1$ of $(H_i)_{i\in I}$ ...

I know that for a 1D function, I can calculate the numerical derivative at every point, $\DeclareMathOperator{\d}{d\!} (x_1,y_1)$, with $\d y/\d x$ where $\d y = y_2 - y_0$ and $\d x = x_2 - x_0$. If ...