Q:

linear map notation question

In Axler's book Linear Algebra Done Right, he uses the symbol $\cal L$ to denote  the set of all linear maps from $V$ to $W$. Is there a different notation (that's maybe easier to write)? Also, is this a common notation, or is it specific to Axler?

A:

Since $K$-linear maps are the (homo)morphisms of the category of $K$-vector spaces, it is perfectly valid (though not very common) to write $\operatorname{Hom}(V,W)$ for the set (in fact $K$-vector space) of linear maps from $V$ to $W$.

