$X$ and $Y$ are $F$-linear and $\dim\_FX=n$ and $\dim\_FY=m$.
If $n\leq m$, does there exist an $F$-linear injective function $f:X\rightarrow Y$?
Well of course, but how do i notate that?

$$f\begin{pmatrix}x\_1\\x\_2\\ \vdots\\x\_n\end{pmatrix}=\begin{pmatrix}x\_1\\x\_2\\ \vdots\\x\_n\\0\\\vdots\\0\end{pmatrix}$$

And am I right that this is from $F^n\to F^m$?

Note: for me it is not clear wether $x\_i$ is element of Y or not, should i instead map $x\_i \to y\_i$?

Also, does $n\leq m$ imply that at least $n$ is finite?