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Is there an established name for the matrices that establish the conditions for a linear combination of $n$ functions $\lbrace f_1(x),\dots,f_n(x)\rbrace$ being the $n$-times smoothly differentiable continuation of a function $g(x)$ for $x=x_0$ after adding an appropriate constant:

$$\begin{pmatrix}\frac{d}{dx}f_1(x_0)&\dots&\frac{d}{dx}f_n(x_0)\\ \vdots & &\vdots\\ \frac{d^n}{dx^n}f_1(x_0) & \dots & \frac{d^n}{dx^n}f_n(x_0)\end{pmatrix}\begin{pmatrix}c_1 \\ \vdots\\ c_n\end{pmatrix} = \begin{pmatrix}g'(x_0)\\ \vdots\\ g^{(n)}(x_0)\end{pmatrix}$$

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    $\begingroup$ According to this Wikipedia page, it would be the derivative of what is sometimes called a "fundamental matrix". $\endgroup$
    – pregunton
    Mar 7, 2020 at 18:40
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    $\begingroup$ @pregunton thank you very much, that ianswers my question $\endgroup$
    – Manfred Weis
    Mar 7, 2020 at 18:47
  • $\begingroup$ @pregunton Could you formulate it as an answer? Answering in comment is not a good practice on Stack Exchange sites. (In addition, you'll get internet points for it your answer.) $\endgroup$
    – Federico Poloni
    Mar 7, 2020 at 19:31
  • $\begingroup$ @FedericoPoloni My apologies. I expanded the comment into an answer. $\endgroup$
    – pregunton
    Mar 7, 2020 at 20:23
  • $\begingroup$ No worries, and thanks! $\endgroup$
    – Federico Poloni
    Mar 7, 2020 at 20:23

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According to this Wikipedia page, the matrix in the question is the derivative of what is sometimes called a fundamental matrix. A Google search of that term together with "Wronskian" gives quite a few relevant hits, so the name seems to be in common use.

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