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: 


$$\begin{pmatrix}\frac{d}{dx}f\_1(x\_0)&\dots&\frac{d}{dx}f\_n(x\_0)\\ \vdots & &\vdots\\ \frac{d^n}{dx^n}f\_1(x\_0) & \dots & \frac{d^n}{dx^n}f\_n(x\_0)\end{pmatrix}\begin{pmatrix}c\_1 \\ \vdots\\ c\_n\end{pmatrix} = \begin{pmatrix}g'(x\_0)\\ \vdots\\ g^{(n)}(x\_0)\end{pmatrix}$$



Name for matrix associated to smooth continuation
According to [this Wikipedia page](https://en.wikipedia.org/wiki/Wronskian#Definition), 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.


