Set of homomorphisms between vector spaces notation

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$V$, $W$ are vector spaces, $K$ is a field.

This may sounds like a very silly question, but I have seen the notation

$$\mathrm{Hom}_K(V,W)$$

which presumably denotes the set of homomorphisms i.e. linear maps between vector spaces. (I’ve only previously seen it written with different notation)

A linear map i.e. homomorphism of vector spaces $f: V \to W$ requires them to be over the same field $K$, so presumably we can also drop the $K$ and write

$$\mathrm{Hom}(V,W)$$

with the first example’s use of $K$ only there for clarity rather than having any different meaning to the second one. Am I correct?