Given a function $f: \mathbb{R}^2\rightarrow\mathbb{C}$ sampled as a matrix $F_{ij}$ on some ractangle $[a,b]\times[c,d]\subset\mathbb{R}^2$ with steps $\Delta x$ and $\Delta y$ as the stepsizes so that
$$ F_{ij} = f(a+i\Delta x, b+j\Delta y) $$
and with $i,j=1,\ldots,N$ so that $F\in\mathbb{C}^{N\times N}$, is there a "simple" condition to put upon $f$ that implies "$F$ is invertible"?
In other words, is there a relationship "$f$ is ??? $\Rightarrow$ "$F$ invertible"?
